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Combinatorial Foundation Of Homology And Homotopy
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Book Synopsis Combinatorial Foundation of Homology and Homotopy by : Hans-Joachim Baues
Download or read book Combinatorial Foundation of Homology and Homotopy written by Hans-Joachim Baues and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new combinatorial foundation of the two concepts, based on a consideration of deep and classical results of homotopy theory, and an axiomatic characterization of the assumptions under which results in this field hold. Includes numerous explicit examples and applications in various fields of topology and algebra.
Book Synopsis Combinatorial Foundation of Homology and Homotopy by : Hans-Joachim Baues
Download or read book Combinatorial Foundation of Homology and Homotopy written by Hans-Joachim Baues and published by . This book was released on 2014-01-15 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Two-Dimensional Homotopy and Combinatorial Group Theory by : Cynthia Hog-Angeloni
Download or read book Two-Dimensional Homotopy and Combinatorial Group Theory written by Cynthia Hog-Angeloni and published by Cambridge University Press. This book was released on 1993-12-09 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.
Book Synopsis Combinatorial Homotopy and 4-dimensional Complexes by : Hans J. Baues
Download or read book Combinatorial Homotopy and 4-dimensional Complexes written by Hans J. Baues and published by Walter de Gruyter. This book was released on 1991 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The bulk of the book is devoted to the algebraic theory of quadratic modules and their connections with 4-dimensional complexes, Pontrjagin squares, homotopy groups, the cohomology of categories, and algebraic K-theory. The first three chapters provide the background needed and may serve as an introduction to basic combinatorial homotopy theory. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Combinatorial And Toric Homotopy: Introductory Lectures by : Alastair Darby
Download or read book Combinatorial And Toric Homotopy: Introductory Lectures written by Alastair Darby and published by World Scientific. This book was released on 2017-10-20 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning.The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics.The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students.
Book Synopsis Computational Homology by : Tomasz Kaczynski
Download or read book Computational Homology written by Tomasz Kaczynski and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.
Book Synopsis Advances in Two-Dimensional Homotopy and Combinatorial Group Theory by : Wolfgang Metzler
Download or read book Advances in Two-Dimensional Homotopy and Combinatorial Group Theory written by Wolfgang Metzler and published by Cambridge University Press. This book was released on 2018 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.
Book Synopsis Combinatorial Algebraic Topology by : Dimitry Kozlov
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.
Book Synopsis Combinatorial Methods in Topology and Algebraic Geometry by : John R. Harper
Download or read book Combinatorial Methods in Topology and Algebraic Geometry written by John R. Harper and published by American Mathematical Soc.. This book was released on 1985 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the areas where combinatorial methods have proven especially fruitful: topology and combinatorial group theory, knot theory, 3-manifolds, homotopy theory and infinite dimensional topology, and four manifolds and algebraic surfaces.
Book Synopsis Equivariant Homotopy and Cohomology Theory by : J. Peter May
Download or read book Equivariant Homotopy and Cohomology Theory written by J. Peter May and published by American Mathematical Soc.. This book was released on 1996 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Book Synopsis Introduction to Combinatorial Torsions by : Vladimir Turaev
Download or read book Introduction to Combinatorial Torsions written by Vladimir Turaev and published by Birkhäuser. This book was released on 2012-12-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.
Book Synopsis Homotopy Type and Homology by : Hans J. Baues
Download or read book Homotopy Type and Homology written by Hans J. Baues and published by Oxford University Press. This book was released on 1996 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph represents an attempt to classify homotopy types of simply connected CW-complexes. It provides methods and examples of explicit homotopy classifications, and includes applications to the classification of manifolds.
Book Synopsis Cohomology Operations and Applications in Homotopy Theory by : Robert E. Mosher
Download or read book Cohomology Operations and Applications in Homotopy Theory written by Robert E. Mosher and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
Book Synopsis Homotopy Theoretic Methods in Group Cohomology by : William G. Dwyer
Download or read book Homotopy Theoretic Methods in Group Cohomology written by William G. Dwyer and published by Birkhäuser. This book was released on 2012-12-06 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups. The course took place at the Centre de Recerca Mathematica (CRM) in Bellaterra from May 27 to June 2, 1998 and was part of an emphasis semester on Algebraic Topology. It consisted of two parallel series of 6 lectures of 90 minutes each and was intended as an introduction to new homotopy theoretic methods in group cohomology. The first part of the book is concerned with methods of decomposing the classifying space of a finite group into pieces made of classifying spaces of appropriate subgroups. Such decompositions have been used with great success in the last 10-15 years in the homotopy theory of classifying spaces of compact Lie groups and p-compact groups in the sense of Dwyer and Wilkerson. For simplicity the emphasis here is on finite groups and on homological properties of various decompositions known as centralizer resp. normalizer resp. subgroup decomposition. A unified treatment of the various decompositions is given and the relations between them are explored. This is preceeded by a detailed discussion of basic notions such as classifying spaces, simplicial complexes and homotopy colimits.
Book Synopsis Stable Homotopy and Generalised Homology by : John Frank Adams
Download or read book Stable Homotopy and Generalised Homology written by John Frank Adams and published by University of Chicago Press. This book was released on 1974 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Book Synopsis Homotopy Theory with Bornological Coarse Spaces by : Ulrich Bunke
Download or read book Homotopy Theory with Bornological Coarse Spaces written by Ulrich Bunke and published by Springer Nature. This book was released on 2020-09-03 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories. It introduces the category of bornological coarse spaces and the notion of a coarse homology theory, and further constructs the universal coarse homology theory. Hybrid structures are introduced as a tool to connect large-scale with small-scale geometry, and are then employed to describe the coarse motives of bornological coarse spaces of finite asymptotic dimension. The remainder of the book is devoted to the construction of examples of coarse homology theories, including an account of the coarsification of locally finite homology theories and of coarse K-theory. Thereby it develops background material about locally finite homology theories and C*-categories. The book is intended for advanced graduate students and researchers who want to learn about the homotopy-theoretical aspects of large scale geometry via the theory of infinity categories.
Book Synopsis Strong Shape and Homology by : Sibe Mardesic
Download or read book Strong Shape and Homology written by Sibe Mardesic and published by Springer Science & Business Media. This book was released on 2000-01-07 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape theory is an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces. Besides applications in topology, it has interesting applications in various other areas of mathematics, especially in dynamical systems and C*-algebras. Strong shape is a refinement of ordinary shape with distinct advantages over the latter. Strong homology generalizes Steenrod homology and is an invariant of strong shape. The book gives a detailed account based on approximation of spaces by polyhedra (ANR's) using the technique of inverse systems. It is intended for researchers and graduate students. Special care is devoted to motivation and bibliographic notes.
