Algebraic Topology Homotopy and Group Cohomology: by Alejandro Adem (auth.), Jaume Aguadé, Manuel Castellet,

By Alejandro Adem (auth.), Jaume Aguadé, Manuel Castellet, Frederick Ronald Cohen (eds.)

The papers during this assortment, all totally refereed, unique papers, mirror many features of contemporary major advances in homotopy thought and team cohomology. From the Contents: A. Adem: at the geometry and cohomology of finite basic groups.- D.J. Benson: Resolutions and Poincar duality for finite groups.- C. Broto and S. Zarati: On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C. Ravenel: Morava K-theories of classifying areas and generalized characters for finite groups.- okay. Ishiguro: Classifying areas of compact basic lie teams and p-tori.- A.T. Lundell: Concise tables of James numbers and a few homotopyof classical Lie teams and linked homogeneous spaces.- J.R. Martino: Anexample of a reliable splitting: the classifying house of the 4-dim unipotent group.- J.E. McClure, L. Smith: at the homotopy strong point of BU(2) on the leading 2.- G. Mislin: Cohomologically valuable components and fusion in groups.

Show description

Read Online or Download Algebraic Topology Homotopy and Group Cohomology: Proceedings of the 1990 Barcelona Conference on Algebraic Topology, held in S. Feliu de Guíxols, Spain, June 6–12, 1990 PDF

Similar topology books

Geometry of Characteristic Classes (Translations of Mathematical Monographs)

Attribute sessions are relevant to the fashionable learn of the topology and geometry of manifolds. They have been first brought in topology, the place, for example, they can be used to outline obstructions to the life of definite fiber bundles. attribute periods have been later outlined (via the Chern-Weil concept) utilizing connections on vector bundles, hence revealing their geometric facet.

Parametrized homotopy theory

This e-book develops rigorous foundations for parametrized homotopy thought, that is the algebraic topology of areas and spectra which are always parametrized through the issues of a base house. It additionally starts off the systematic examine of parametrized homology and cohomology theories. The parametrized international offers the common domestic for plenty of classical notions and effects, comparable to orientation conception, the Thom isomorphism, Atiyah and Poincaré duality, move maps, the Adams and Wirthmüller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences.

Models for Smooth Infinitesimal Analysis

The purpose of this publication is to build different types of areas which comprise the entire C? -manifolds, but additionally infinitesimal areas and arbitrary functionality areas. To this finish, the recommendations of Grothendieck toposes (and the good judgment inherent to them) are defined at a leisurely speed and utilized. by way of discussing themes equivalent to integration, cohomology and vector bundles within the new context, the adequacy of those new areas for research and geometry may be illustrated and the relationship to the classical method of C?

Additional resources for Algebraic Topology Homotopy and Group Cohomology: Proceedings of the 1990 Barcelona Conference on Algebraic Topology, held in S. Feliu de Guíxols, Spain, June 6–12, 1990

Sample text

Let B ( P ) be the involutory permutation of E in which e hi and ~h are corresponding points. An arbitrary numbering of the elements of E around each vertex ei (resp. ~i) determines a permutation C ( P ) of E whose orbit sets are Ei, Ei. With the above notation, we have the following result proved in [14]. T H E O R E M 1. K(P) is a spine of a closed prime orientable 3-manifold M(P) if and only if the permutation group generated by A ( P ) C ( P ) and B ( P ) C ( P ) (resp. A ( P ) and C ( P ) ) is transitive and the relation IA(P)I - IC(P)[ + 2 = IA(P)C(P)I holds.

It is easy to show that the algebra of invariants Rs(K) c is now the integral closure of A/~-X(K) in its field of fractions. As a consequence, if K in the corollary above is integrally closed we also have K = Rm(K) a. Proof of theorem: Let K be a connected unstable A~-algebra. Properties (1) and (2) ensure that there exists an elementary abelian 2-group V with dimension the krulldimension of K and an embedding K C H ' V , [AW]. of K is the algebra of invariants: H*V c ([AW] [BZ]). C~m+lH*V) G i2 , Af~I(K ) ) Rm(K) c The inclusions K C

17 P r o p o s i t i o n . /~fil m-clOsed, and N is (exactly) j-reduced and A/iln-closed. Then, M ® N is (exactly) (i + j)-reduced and A/ilm~xl( i+,),(j+m) } -closed. " We already know M ® N is (exactly) (i + j)-reduced. Suppose (n + i) _> (m + j). Let N --* A/j-I(N) ~ C be the A/i/j-localization of N. Then, for k > j, ~kC ~-- (R~Ek)(N), so 'C is (exactly) n-reduced. Now we consider the exact sequence 0 ~ M ® N ~ M ® A/TI(N) ~ M ® C ~ 0. )-closed. 18 P r o p o s i t i o n . Every projective limit of A/ilm-closed objects is A/ilm-elosed.

Download PDF sample

Rated 4.27 of 5 – based on 17 votes