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Friday, May 8, 2020 | History

2 edition of Equivariant Singular Homology & Cohomology I (Memoirs of the American Mathematical Society; No. 156) found in the catalog.

Equivariant Singular Homology & Cohomology I (Memoirs of the American Mathematical Society; No. 156)

by Soren Illman

  • 344 Want to read
  • 40 Currently reading

Published by American Mathematical Society .
Written in English

    Subjects:
  • Advanced,
  • Homology theory,
  • Mathematics

  • The Physical Object
    FormatPaperback
    Number of Pages74
    ID Numbers
    Open LibraryOL11419850M
    ISBN 100821818562
    ISBN 109780821818565

    Equivariant cohomology Non-equivariant cohomology The inverse problem Spatial polygon spaces and conjugation spaces Equivariant characteristic classes The equivariant cohomology of certain homogeneous spaces The Kervaire invariant Exercises for Chapter 10 EQUIVARIANT STABLE HOMOTOPY THEORY J.P.C. GREENLEES AND J.P. MAY Contents Introduction 1 1. Equivariant homotopy 2 2. The equivariant stable homotopy category 10 3. Homology and cohomology theories and fixed point spectra 15 4. Change of groups and duality theory 20 5. Mackey functors, K(M,n)’s, and RO(G)-graded cohomology 25 6.

    Singular homology is homology with compact supports, in the sense that the groups associated with are equal to the direct limits of the homology groups of the compact sets. Singular cohomology is defined in a dual way. The cochain complex is defined as the complex of homomorphisms into of the integral singular chain complex. Buy Mod Two Homology and Cohomology (Universitext) on FREE SHIPPING on qualified orders Mod Two Homology and Cohomology (Universitext): Hausmann, Jean-Claude: : BooksCited by:

    We define and study equivariant periodic cyclic homology for locally compact groups. This can be viewed as a noncommutative generalization of equivariant de Rham cohomology. Although the construction resembles the Cuntz-Quillen approach to ordinary cyclic homology, a completely new feature in the equivariant setting is the fact that the basic.   The equivariant closed forms were introduced by Henri Cartan thirty years earlier to study the cohomology of a space with a group action, called equivariant cohomology.


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Equivariant Singular Homology & Cohomology I (Memoirs of the American Mathematical Society; No. 156) by Soren Illman Download PDF EPUB FB2

Get this from a library. Equivariant singular homology and cohomology. [Sören Illman] -- Let G be a topological group. We construct an equivariant homology and equivariant cohomology theory, defined on the category of all G-pairs and G-maps, which both satisfy all seven equivariant.

Introduction Part I. Equivariant singular theory 1. Coefficient systems 2. The existence theorems for equivariant singular homology and cohomology 3. Construction of equivariant singular homology 4. Construction of equivariant singular cohomology 5. The homotopy axiom 6. The excision axiom 7.

The dimension axiom 8. Additivity properties Part II. There is an algebraic topology book that specializes particularly in homology theory-namely, James Vick's Homology Theory:An Introduction To Algebraic does a pretty good job of presenting singular homology theory from an abstract,modern point of view, but with plenty of pictures.

In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a group can be viewed as a common generalization of group cohomology and an ordinary cohomology ically, the equivariant cohomology ring of a space with action of a topological group is defined as the ordinary cohomology.

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.

In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups ().

Intuitively, singular homology counts, for each dimension n, the n-dimensional holes of a ar homology is a particular example of a homology theory, which has now grown to be a rather broad. Aimed at advanced graduate students and researchers in algebraic topology and related fields, the book assumes knowledge of basic algebraic topology and group actions.

Keywords 55N91, 55P91, 57R91, 55N25, 55P42, 55P20, 55R70, 55R91 Homology equivariant ordinary cell complex. Cite this paper as: Illman S. () Equivariant singular homology and cohomology for actions of compact lie groups.

In: Ku H.T., Mann L.N., Sicks J.L., Su J.C. (eds) Proceedings of the Second Conference on Compact Transformation by: i.

equivariant singular theory 3 7 free; 1. coefficient systems 3 7; 2. the existence theorems for equivariant singular homology and c0h0m0l0gy 4 8; 3. construction of equivariant singular homology 10 14; 4.

construction of equivariant singular cohomology 17 21; 5. the h0m0t0py axiom 24 28; 6. the excision axiom 29 33; 7. the dimension axiom This paper provides an introduction to equivariant cohomology and homology using the approach of Goresky, Kottwitz, and MacPherson. When a group G acts suitably on a variety X, the equivariant cohomology of X can be computed using the combinatorial data of a skeleton of G-orbits on X.

We give both a geometric definition and the traditional definition of equivariant cohomology. We include a Cited by: Singular cohomology. Singular cohomology is a powerful invariant in topology, associating a graded-commutative ring to any topological space.

Every continuous map f: X → Y determines a homomorphism from the cohomology ring of Y to that of X; this puts strong restrictions on the possible maps from X to more subtle invariants such as homotopy groups, the cohomology ring tends to be.

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. Key words and phrases.

equivariant homology, free loop space, string topology, Tate cohomology, stratifold. The first named author was partially supported by KAKENHI, Grant-in. What is called Bredon cohomology after is the flavor of G G-equivariant cohomology which uses the “fine” equivariant homotopy theory of topological G-spaces that by Elmendorf's theorem is equivalent to the homotopy theory of (∞,1)-presheaves over G G-orbit category, instead of.

We consider ex-G-spaces over B and grade all homology and cohomology on RO(ΠB), the equivariant fundamental groupoid of B. Details on ΠB as well as RO(ΠB) can be found in both [3] and [2. EQUIVARIANT CHARACTERISTIC CLASSES OF SINGULAR COMPLEX ALGEBRAIC VARIETIES SYLVAIN E.

CAPPELL, LAURENTIU MAXIM, JORG SCH URMANN, AND JULIUS L. SHANESON book [H66], Hirzebruch provided a unifying theory of (cohomology) characteristic classes One of the aims of this note is to construct an equivariant theory of homology Hirzebruch classes.

Introduction to Equivariant Cohomology in Algebraic Geometry Dave Anderson Ap Abstract Introduced by Borel in the late ’s, equivariant cohomology en-codes information about how the topology of a space interacts with a group action. Quite some time passed before algebraic geometers picked up on these ideas, but in the last.

Title: Equivariant ordinary homology and cohomology Authors: Steven R. Costenoble, Stefan Waner (Submitted on 16 Oct (v1), last revised 2 Dec (this version, v3))Cited by: The de Rham theorem states that this mapping is an isomorphism, so that the de Rham and singular cohomology groups with real coefficients are identical for manifolds.

This allows us to deduce information about forms from topological properties. Equivariant cohomology and equivariant intersection theory Michel Brion This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D.

Edidin and W. Graham. Our main aim is to obtain explicit descriptions of. homological-algebra topological-quantum-field-theory equivariant-cohomology cyclic-homology string-topology. asked Dec 22 '18 at kyler. 51 1 1 bronze badge. 4. reference-request aic-topology equivariant-cohomology equivariant-homotopy stable-homotopy-category.

Newest equivariant-cohomology questions feed.Singular Homology 1. Homology, Introduction In the beginning, we suggested the idea of attaching algebraic ob-jects to topological spaces in order to discern their properties.

In lan-guage introduced later, we want functors from the category of topo-logical spaces (or perhaps some related category) and continuous mapsFile Size: KB.Equivariant Cohomology HC We have an equivalent description of equivariant cohomology using a kind of equivariant generalization of singular chains; we can get to equivariant cohomology by dualizing the resulting complex, but let i.e.

a module over the homology algebra Later we will be interested verifying the condition that the action of H.