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Sunday, July 19, 2020 | History

4 edition of Equivalences of classifying spaces completed at the prime two found in the catalog. # Equivalences of classifying spaces completed at the prime two

## by Robert Oliver

Written in

Subjects:
• Classifying spaces.,
• Localization theory.,
• Finite simple groups.

• Edition Notes

Classifications The Physical Object Statement Bob Oliver. Series Memoirs of the American Mathematical Society,, no. 848 LC Classifications QA3 .A57 no. 848, QA612.6 .A57 no. 848 Pagination p. cm. Open Library OL3432146M ISBN 10 0821838288 LC Control Number 2005058189

On K(n)-equivalences of spaces A.K. Bousﬁeld Abstract. Working at a ﬁxed prime p, we show that each K(n)∗-equivalence of spaces is a K(m)∗-equivalence for 1 ≤ m ≤ n. Our proof uses homotopical localiza-tion theory and depends on the K(n)∗-nonacyclicily of the highly connected inﬁnite loop spaces in the associated Ω-spectrum of k(m). In topology and related branches of mathematics, a Hausdorff space, separated space or T 2 space is a topological space where for any two distinct points there exist neighbourhoods of each which are disjoint from each other. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T 2) is the most frequently used and discussed.T: (Kolmogorov).

The proof of Theorem A was completed by Voevodsky in the –11 papers V-EM [Voe10c] and MC/l [Voe11], but depends on the work of many other people. See the Historical notes at the end of Chapter chapterI 1 for details. For any smooth variety Xover k, we can form the bigraded motivic coho-. the basic equivalences in somewhat the same way you use algebraic rules like 2x 3x= xor (x+ 1)(x 3) x 3 = x+ 1. Exercise Use the propositional equivalences in the list of important logical equivalences above to prove [(p!q) ^:q]!:pis a tautology. Exercise Use truth tables to verify De Morgan’s Laws. Simplifying Size: KB.

a third space Z, and mod p equivalences X > Z space (Definition ) of the action of Tipq on BG(C)p. By our Theorem , if X is a p-complete space which satisfies certain technical conditions. The arrows are ‘realization functors’ determined by the underlying spaces. In this language, the problem is to take a topological vector bundle—an object on the right—and lift it all the way to the left to get an algebraic vector bundle. In the topological case one can study G-vector bundles as maps into the classifying space Size: 2MB.

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Free Online Library: Equivalences of classifying spaces completed at the prime two.(Brief Article, Book Review) by "SciTech Book News"; Publishing industry Library and information science Science and technology, general.

Printer Friendly. 24, articles and books. Abstract: We prove here the Martino-Priddy conjecture at the prime \(2\): the \(2\)-completions of the classifying spaces of two finite groups \(G\) and \(G'\) are homotopy equivalent if and only if there is an isomorphism between their Sylow \(2\)-subgroups which preserves fusion.

Get this from a library. Equivalences of classifying spaces completed at the prime two. [Robert Oliver]. Equivalences of classifying spaces completed at the prime two.

[Robert Oliver] -- Introduction Higher limits over orbit categories Reduction to simple groups A relative version of \$\Lambda\$-functors Subgroups which contribute to higher limits Alternating groups Groups of Lie type. to have shown that for any prime pand any pair G,G0 of ﬁnite groups, the p-completed classifying spaces BG∧ p and BG0∧ p are homotopy equivalent if and only if the p-local structures of Gand of G0 are isomorphic in a sense to be made precise below.

This was part of a program by those two authors and others to understand. Classification Dewey: s. Olivier, Bob () (Auteur / author) Collection: Memoirs of the American Mathematical Society / Providence (R.I.): American Mathematical Society, Relation: Equivalences of classifying spaces completed at the prime two / Bob Olivier / Providence (R.I.): American Mathematical Society, Equivalences of Classifying Spaces Completed at the Prime Two, Issue Bob Oliver, Robert Oliver No preview available - Recent Developments in Quantum Affine Algebras.

Fix a prime p. A mod-p homotopy group extension of a group π by a group G is a fibration with base space Bπp∧ and fibre BGp∧. In this paper we study h Cited by: Bob Oliver, Equivalences of classifying spaces completed at odd primes.

David Blanc and George Peschke, The plus construction, Postnikov towers and universal central module extensions. Louis McAuley,The Hilbert-Smith conjecture. Equivalences of classifying spaces completed at the prime two (Amer.

Math. Soc. Memoirs) (version du 31/12/04) (avec H. Fausk) Continuity of π-perfection for compact Lie groups (Bull. London Math. Soc., 37,). Two compact Lie groups G and H are isomorphic if and only if their classifying spaces BG and BH are homotopy equivalent [Mø02] [Os92] [No95].

The equivalences at the rational level are. homotopy xed space (De nition ) of the action of ˝ q on BG(C)^ p. By our Theoremif Xis a p-complete space which satis es certain technical conditions, then for any pair of self equivalences and such that h i= h iin Out(X), Xh ’Xh.

Here, Out(X) is the group of homotopy classes of self equivalences. for a simple Lie “type” G, and q and q0 are prime powers, both prime to p, which generate the same closed subgroup of p-adic units. Our proof uses homotopy theoretic properties of the p-completed classifying spaces of G and G0, and we know of no purely algebraic proof of this result.

When Gis a ﬁnite group and pis a prime, the fusion system F. In all cases, this will be done by showing that the p-completed classifying spaces of the two groups are homotopy equivalent. A theorem of Martino and Priddy (Theorem below) then implies that the fusion systems are isotypically equivalent.

Since p-completion of spaces plays a central role in our proofs, we give a very brief outline. Again, the classifying space can be represented as a quotient of a hyperplane complement. See papers of Brieskorn-Saito and Deligne from the early 70s. \$\endgroup\$ – Chris Brav Feb 24 '11 at 2.

Two p-completed classifying spaces BG p ∧ and BG’ p ∧ have the same homotopy type if and only if the associated categories ℒ p c (G) and ℒ p c (G’) are : Justin Lynd.

Two models for the classifying space of a subgroup via the geometric bar construction. Ask Question Asked 1 year ago. Active 1 year ago. Viewed times 6 \$\begingroup\$ Let Your bar constructions are just the classifying spaces of these three groupoids, and equivalences between these categories will induce homotopy equivalences.

Equivalences of Classifying Spaces Completed at the Prime Two (Memoirs of the American Mathematical Society) by Robert Oliver ISBN (). Table of Contents. Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type by Carles Broto, Jesper M.

Møller, and Bob Oliver. Introduction. CHAPTER 1. CLASSIFYING SPACES AND COBORDISM A. Bundles with fiber F and structure group n 3 B. The classifying spaces for the classical Lie groups 9 C.

The cobordism classification of closed manifolds 14 D. Oriented cobordism theories and localization 21 E. Connections between cobordism and characteristic classes 24 CllAPTER 2.

Books at Amazon. The Books homepage helps you explore Earth's Biggest Bookstore without ever leaving the comfort of your couch. Here you'll find current best sellers in books, new releases in books, deals in books, Kindle eBooks, Audible audiobooks, and so much more.Topology Vol.

16, pp. Pergamon Press Printed in Great Britain MAPS BETWEEN LOCALIZED HOMOGENEOUS SPACES ERIC M. FRIEDLANDER* (Received 2 December ) IN A previous paper, we employed techniques and maps from algebraic geometry to provide homotopy equivalences between localized classifying spaces of complex reductive algebraic by: The book closes with Part seven, which is called ’Vistas’.

Four main topics are pre-sented: Localizations and completions of spaces, exponents for homotopy groups, classes of spaces and a theme and variations on Miller’s theorem of the triviality of the space of pointed maps from the classifying space of a cyclic group of prime order to a.