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Noetherian loop spaces

Natàlia Castellana, Juan Crespo, Jérôme Scherer (2011)

Journal of the European Mathematical Society

The class of loop spaces of which the mod p cohomology is Noetherian is much larger than the class of p -compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as ℂ P ∞ and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space B X of such an object and prove it is as small as expected, that is, comparable to that of B ℂ P ∞ . We also show that B X differs basically from the classifying space of a p -compact group...

On certain homotopy actions of general linear groups on iterated products

Ran Levi, Stewart Priddy (2001)

Annales de l’institut Fourier

The n -fold product X n of an arbitrary space usually supports only the obvious permutation action of the symmetric group Σ n . However, if X is a p -complete, homotopy associative, homotopy commutative H -space one can define a homotopy action of GL n ( ℤ p ) on X n . In various cases, e.g. if multiplication by p r is null homotopic then we get a homotopy action of G L n ( ℤ / p r ) for some r . After one suspension this allows one to split X n using idempotents of 𝔽 p GL n ( ℤ / p ) which can be lifted to 𝔽 p GL n ( ℤ / p r ) . In fact all of this is possible if X is an H -space...

Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups

Assaf Libman (2011)

Fundamenta Mathematicae

Let G be a compact Lie group. We present a criterion for the orbit spaces of two G-spaces to be homotopy equivalent and use it to obtain a quick proof of Webb’s conjecture for compact Lie groups. We establish two Minami type formulae which present the p-localised spectrum Σ ∞ B G ₊ as an alternating sum of p-localised spectra Σ ∞ B H ₊ for subgroups H of G. The subgroups H are calculated from the collections of the non-trivial elementary abelian p-subgroups of G and the non-trivial p-radical subgroups of G. We...

Quantum classifying spaces and universal quantum characteristic classes

Mićo Đurđević (1997)

Banach Center Publications

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced and analyzed. Interrelations with the abstract algebraic theory of quantum characteristic classes are discussed. Various non-equivalent approaches to defining universal characteristic classes are outlined.

Salvetti complex, spectral sequences and cohomology of Artin groups

Filippo Callegaro (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The aim of this short survey is to give a quick introduction to the Salvetti complex as a tool for the study of the cohomology of Artin groups. In particular we show how a spectral sequence induced by a filtration on the complex provides a very natural and useful method to study recursively the cohomology of Artin groups, simplifying many computations. In the last section some examples of applications are presented.

Self homotopy equivalences of classifying spaces of compact connected Lie groups

Stefan Jackowski, James McClure, Bob Oliver (1995)

Fundamenta Mathematicae

We describe, for any compact connected Lie group G and any prime p, the monoid of self maps B G p → B G p which are rational equivalences. Here, B G p denotes the p-adic completion of the classifying space of G. Among other things, we show that two such maps are homotopic if and only if they induce the same homomorphism in rational cohomology, if and only if their restrictions to the classifying space of the maximal torus of G are homotopic.

Currently displaying 61 – 80 of 102