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Equivariant Cohomology Of Configuration Spaces Mod 2
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Book Synopsis Equivariant Cohomology of Configuration Spaces Mod 2 by : Pavle V. M. Blagojević
Download or read book Equivariant Cohomology of Configuration Spaces Mod 2 written by Pavle V. M. Blagojević and published by Springer Nature. This book was released on 2022-01-01 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(R^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F(R^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper. This invalidates a paper by three of the authors, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and l-skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker. Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry.
Book Synopsis Mod Two Homology and Cohomology by : Jean-Claude Hausmann
Download or read book Mod Two Homology and Cohomology written by Jean-Claude Hausmann and published by Springer. This book was released on 2015-01-08 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: 1. It leads more quickly to the essentials of the subject, 2. An absence of signs and orientation considerations simplifies the theory, 3. Computations and advanced applications can be presented at an earlier stage, 4. Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduate-level introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between Stiefel-Whitney classes and Schubert calculus. More recent developments are also covered, including topological complexity, face spaces, equivariant Morse theory, conjugation spaces, polygon spaces, amongst others. Each chapter ends with exercises, with some hints and answers at the end of the book.
Download or read book Braids written by Joan S. Birman and published by American Mathematical Soc.. This book was released on 1988 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group, held at the University of California, Santa Cruz, in July 1986. This work is suitable for graduate students and researchers who wish to learn more about braids, as well as more experienced workers in this area.
Book Synopsis Geometric Applications of Homotopy Theory II by : M.G. Barratt
Download or read book Geometric Applications of Homotopy Theory II written by M.G. Barratt and published by Springer. This book was released on 2006-11-15 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1770 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Applications of Homotopy Theory I by : M. G. Barratt
Download or read book Geometric Applications of Homotopy Theory I written by M. G. Barratt and published by Springer. This book was released on 2006-11-15 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Modeling of Topological and Computational Structures and Applications by : Sofia Lambropoulou
Download or read book Algebraic Modeling of Topological and Computational Structures and Applications written by Sofia Lambropoulou and published by Springer. This book was released on 2017-12-14 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a workshop in connection with the research project Thales on Algebraic Modeling of Topological and Computational Structures and Applications, held at the National Technical University of Athens, Greece in July 2015. The reader will benefit from the innovative approaches to tackling difficult questions in topology, applications and interrelated research areas, which largely employ algebraic tools.
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 Introductory Lectures on Equivariant Cohomology by : Loring W. Tu
Download or read book Introductory Lectures on Equivariant Cohomology written by Loring W. Tu and published by Princeton University Press. This book was released on 2020-03-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.
Download or read book Vietnam Journal of Mathematics written by and published by . This book was released on 2002 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Acta Mathematica Vietnamica written by and published by . This book was released on 1982 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Methods in Nonlinear Analysis by :
Download or read book Topological Methods in Nonlinear Analysis written by and published by . This book was released on 1998 with total page 818 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Equivariant Cohomology of Configurations in $ R^ N $ by : G. I. Lehrer
Download or read book Equivariant Cohomology of Configurations in $ R^ N $ written by G. I. Lehrer and published by . This book was released on 1999 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Configuration Spaces by : Anders Björner
Download or read book Configuration Spaces written by Anders Björner and published by Springer. This book was released on 2013-12-18 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May-June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians.
Book Synopsis Equivariant Cohomology in Algebraic Geometry by : David Anderson
Download or read book Equivariant Cohomology in Algebraic Geometry written by David Anderson and published by Cambridge University Press. This book was released on 2023-10-26 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.
Book Synopsis Algebraic Topology and Transformation Groups by : Tammo tom Dieck
Download or read book Algebraic Topology and Transformation Groups written by Tammo tom Dieck and published by Mathematica Gottingensis. This book was released on 1988-11-23 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: S. Bauer: The homotopy type of a 4-manifold with finite fundamental group.- C.-F. Bödigheimer, F.R. Cohen: Rational cohomology of configuration spaces of surfaces.- G. Dylawerski: An S1 -degree and S1 -maps between representation spheres.- R. Lee, S.H. Weintraub: On certain Siegel modular varieties of genus two and levels above two.- L.G. Lewis, Jr.: The RO(G)-graded equivariant ordinary cohomology of complex projective spaces with linear /p actions.- W. Lück: The equivariant degree.- W. Lück, A. Ranicki: Surgery transfer.- R.J. Milgram: Some remarks on the Kirby - Siebenmann class.- D. Notbohm: The fixed-point conjecture for p-toral groups.- V. Puppe: Simply connected manifolds without S1-symmetry.- P. Vogel: 2 x 2 - matrices and application to link theory.
Book Synopsis On Rational Bredon Cohomology by : Qiaofeng Zhu
Download or read book On Rational Bredon Cohomology written by Qiaofeng Zhu and published by . This book was released on 2019 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Bredon cohomology is a cohomology theory that applies to topological spaces equipped with the group actions. The thesis is directed towards computation of rational Bredon cohomology of equivariant polyhedral products and equivariant configuration spaces in the case when the acting groups are small non-abelian groups. A polyhedral product is a natural subspace of a Cartesian product, which is specified by a simplicial complex K. The automorphism group Aut(K) of K induces a group action on the polyhedral product. In the thesis we study this group action and give a formula for the fixed point set of the polyhedral product for any subgroup H of Aut(K). We use the fixed point data to compute examples of Bredon cohomology. A configuration space of a topological space X refers to the topological space of pairwise distinct points in X. For any group G, given a real linear representation V , the configuration space of V has a natural diagonal G- action. In the thesis we study this group action on the configuration space and give a decomposition of the homology Bredon coefficient system of the configuration space and apply this to compute Bredon cohomology of the configuration space."--Pages vi-vii.
