Algebraic & Geometric Topology

Lusternik–Schnirelmann category and the connectivity of $X$

Nicholas A Scoville

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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.

Article information

Source
Algebr. Geom. Topol., Volume 12, Number 1 (2012), 435-448.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715345

Digital Object Identifier
doi:10.2140/agt.2012.12.435

Mathematical Reviews number (MathSciNet)
MR2916282

Zentralblatt MATH identifier
1250.55001

Subjects
Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space 55P05: Homotopy extension properties, cofibrations

Keywords
Lusternik–Schnirelmann category categorical sequence cone length killing length Egyptian fractions mapping cone sequence

Citation

Scoville, Nicholas A. Lusternik–Schnirelmann category and the connectivity of $X$. Algebr. Geom. Topol. 12 (2012), no. 1, 435--448. doi:10.2140/agt.2012.12.435. https://projecteuclid.org/euclid.agt/1513715345


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