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2012 Lusternik–Schnirelmann category and the connectivity of $X$
Nicholas A Scoville
Algebr. Geom. Topol. 12(1): 435-448 (2012). DOI: 10.2140/agt.2012.12.435

Abstract

We define and study a homotopy invariant called the connectivity weight to compute the weighted length between spaces X and Y. This is an invariant based on the connectivity of Ai, where Ai is a space attached in a mapping cone sequence from X to Y. We use the Lusternik–Schnirelmann category to prove a theorem concerning the connectivity of all spaces attached in any decomposition from X to Y. This theorem is used to prove that for any positive rational number q, there is a space X such that q= clω(X), the connectivity weighted cone-length of X. We compute clω(X) and klω(X) for many spaces and give several examples.

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Nicholas A Scoville. "Lusternik–Schnirelmann category and the connectivity of $X$." Algebr. Geom. Topol. 12 (1) 435 - 448, 2012. https://doi.org/10.2140/agt.2012.12.435

Information

Received: 25 August 2011; Revised: 8 December 2011; Accepted: 8 December 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1250.55001
MathSciNet: MR2916282
Digital Object Identifier: 10.2140/agt.2012.12.435

Subjects:
Primary: 55M30, 55P05

Rights: Copyright © 2012 Mathematical Sciences Publishers

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Vol.12 • No. 1 • 2012
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