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Author : Xun Dong
Publisher :
ISBN 13 :
Total Pages : 150 pages
Book Rating : 4.:/5 (319 download)
Download or read book The Topology of Bounded Degree Graph Complexes and Finite Free Resolutions written by Xun Dong and published by . This book was released on 2001 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jakob Jonsson
Publisher : Springer
ISBN 13 : 3540758593
Total Pages : 376 pages
Book Rating : 4.5/5 (47 download)
Download or read book Simplicial Complexes of Graphs written by Jakob Jonsson and published by Springer. This book was released on 2007-12-10 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.
Author : Mikhail Lyubich
Publisher : American Mathematical Soc.
ISBN 13 : 0821836668
Total Pages : 443 pages
Book Rating : 4.8/5 (218 download)
Download or read book Graphs and Patterns in Mathematics and Theoretical Physics written by Mikhail Lyubich and published by American Mathematical Soc.. This book was released on 2005 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Stony Brook Conference, "Graphs and Patterns in Mathematics and Theoretical Physics", was dedicated to Dennis Sullivan in honor of his sixtieth birthday. The event's scientific content, which was suggested by Sullivan, was largely based on mini-courses and survey lectures. The main idea was to help researchers and graduate students in mathematics and theoretical physics who encounter graphs in their research to overcome conceptual barriers. The collection begins with Sullivan's paper, "Sigma models and string topology," which describes a background algebraic structure for the sigma model based on algebraic topology and transversality. Other contributions to the volume were organized into five sections: Feynman Diagrams, Algebraic Structures, Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects of Dynamics, and Physics. These sections, along with more research-oriented articles, contain the following surveys: "Feynman diagrams for pedestrians and mathematicians" by M. Polyak, "Notes on universal algebra" by A. Voronov, "Unimodal maps and hierarchical models" by M. Yampolsky, and "Quantum geometry in action: big bang and black holes" by A. Ashtekar. This comprehensive volume is suitable for graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.
Author : Jakob Jonsson
Publisher : Springer Science & Business Media
ISBN 13 : 3540758585
Total Pages : 376 pages
Book Rating : 4.5/5 (47 download)
Download or read book Simplicial Complexes of Graphs written by Jakob Jonsson and published by Springer Science & Business Media. This book was released on 2007-11-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.
Author :
Publisher :
ISBN 13 :
Total Pages : 784 pages
Book Rating : 4.F/5 ( download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2003 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Warren Dicks
Publisher : Cambridge University Press
ISBN 13 : 9780521230339
Total Pages : 304 pages
Book Rating : 4.2/5 (33 download)
Download or read book Groups Acting on Graphs written by Warren Dicks and published by Cambridge University Press. This book was released on 1989-03-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1989, this is an advanced text and research monograph on groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the topology becomes graph theory. Two-dimensional topics include the characterization of Poincare duality groups and accessibility of almost finitely presented groups. The main three-dimensional topics are the equivariant loop and sphere theorems. The prerequisites grow as the book progresses up the dimensions. A familiarity with group theory is sufficient background for at least the first third of the book, while the later chapters occasionally state without proof and then apply various facts which require knowledge of homological algebra and algebraic topology. This book is essential reading for anyone contemplating working in the subject.
Author : P. J. Giblin
Publisher : Chapman & Hall
ISBN 13 :
Total Pages : 358 pages
Book Rating : 4.3/5 (91 download)
Download or read book Graphs, Surfaces, and Homology written by P. J. Giblin and published by Chapman & Hall. This book was released on 1977 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 816 pages
Book Rating : 4.3/5 (91 download)
Download or read book American Doctoral Dissertations written by and published by . This book was released on 2000 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. P. May
Publisher : University of Chicago Press
ISBN 13 : 9780226511832
Total Pages : 262 pages
Book Rating : 4.5/5 (118 download)
Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Author : Edwin H. Spanier
Publisher : Springer Science & Business Media
ISBN 13 : 0387944265
Total Pages : 548 pages
Book Rating : 4.3/5 (879 download)
Download or read book Algebraic Topology written by Edwin H. Spanier and published by Springer Science & Business Media. This book was released on 1989 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.
Author : Herbert Edelsbrunner
Publisher : American Mathematical Society
ISBN 13 : 1470467690
Total Pages : 241 pages
Book Rating : 4.4/5 (74 download)
Download or read book Computational Topology written by Herbert Edelsbrunner and published by American Mathematical Society. This book was released on 2022-01-31 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Author : Dimitry Kozlov
Publisher : Springer Science & Business Media
ISBN 13 : 9783540730514
Total Pages : 416 pages
Book Rating : 4.7/5 (35 download)
Download or read book Combinatorial Algebraic Topology written by Dimitry Kozlov and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
Author : Remco van der Hofstad
Publisher : Cambridge University Press
ISBN 13 : 110717287X
Total Pages : 341 pages
Book Rating : 4.1/5 (71 download)
Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2016-12-22 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Author : Victor Reiner
Publisher : American Mathematical Soc.
ISBN 13 : 0821825259
Total Pages : 146 pages
Book Rating : 4.8/5 (218 download)
Download or read book Quotients of Coxeter Complexes and $P$-Partitions written by Victor Reiner and published by American Mathematical Soc.. This book was released on 1992 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a study of some of the combinatorial and topological properties of finite Coxeter complexes. The author begins by studying some of the general topological and algebraic properties of quotients of Coxeter complexes, and determines when they are pseudomanifolds (with or without boundary) and when they are Cohen-Macaulay or Gorenstein over a field. The paper also examines quotients of Coxeter complexes by cyclic subgroups generated by Coxeter elements.
Author : Tamal Krishna Dey
Publisher : Cambridge University Press
ISBN 13 : 1009103199
Total Pages : 456 pages
Book Rating : 4.0/5 (91 download)
Download or read book Computational Topology for Data Analysis written by Tamal Krishna Dey and published by Cambridge University Press. This book was released on 2022-03-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Author : Caroline J. Klivans
Publisher : CRC Press
ISBN 13 : 135180099X
Total Pages : 296 pages
Book Rating : 4.3/5 (518 download)
Download or read book The Mathematics of Chip-Firing written by Caroline J. Klivans and published by CRC Press. This book was released on 2018-11-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematics of Chip-firing is a solid introduction and overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. The Fundamental properties of chip-firing are covered from a variety of perspectives. This gives the reader both a broad context of the field and concrete entry points from different backgrounds. Broken into two sections, the first examines the fundamentals of chip-firing, while the second half presents more general frameworks for chip-firing. Instructors and students will discover that this book provides a comprehensive background to approaching original sources. Features: Provides a broad introduction for researchers interested in the subject of chip-firing The text includes historical and current perspectives Exercises included at the end of each chapter About the Author: Caroline J. Klivans received a BA degree in mathematics from Cornell University and a PhD in applied mathematics from MIT. Currently, she is an Associate Professor in the Division of Applied Mathematics at Brown University. She is also an Associate Director of ICERM (Institute for Computational and Experimental Research in Mathematics). Before coming to Brown she held positions at MSRI, Cornell and the University of Chicago. Her research is in algebraic, geometric and topological combinatorics.
Author : Roberto Frigerio
Publisher : American Mathematical Soc.
ISBN 13 : 1470441462
Total Pages : 193 pages
Book Rating : 4.4/5 (74 download)
Download or read book Bounded Cohomology of Discrete Groups written by Roberto Frigerio and published by American Mathematical Soc.. This book was released on 2017-11-21 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of bounded cohomology, introduced by Gromov in the late 1980s, has had powerful applications in geometric group theory and the geometry and topology of manifolds, and has been the topic of active research continuing to this day. This monograph provides a unified, self-contained introduction to the theory and its applications, making it accessible to a student who has completed a first course in algebraic topology and manifold theory. The book can be used as a source for research projects for master's students, as a thorough introduction to the field for graduate students, and as a valuable landmark text for researchers, providing both the details of the theory of bounded cohomology and links of the theory to other closely related areas. The first part of the book is devoted to settling the fundamental definitions of the theory, and to proving some of the (by now classical) results on low-dimensional bounded cohomology and on bounded cohomology of topological spaces. The second part describes applications of the theory to the study of the simplicial volume of manifolds, to the classification of circle actions, to the analysis of maximal representations of surface groups, and to the study of flat vector bundles with a particular emphasis on the possible use of bounded cohomology in relation with the Chern conjecture. Each chapter ends with a discussion of further reading that puts the presented results in a broader context.
