Algebraic & Geometric Topology

The LS category of the product of lens spaces

Alexander N Dranishnikov

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Abstract

We reduce Rudyak’s conjecture that a degree-one map between closed manifolds cannot raise the Lusternik–Schnirelmann category to the computation of the category of the product of two lens spaces Lpn × Lqn with relatively prime p and q. We have computed cat(Lpn × Lqn) for values p, q > n2. It turns out that our computation supports the conjecture.

For spin manifolds M we establish a criterion for the equality catM = dimM 1, which is a K–theoretic refinement of the Katz–Rudyak criterion for catM = dimM. We apply it to obtain the inequality cat(Lpn × Lqn) 2n 2 for all odd n and odd relatively prime p and q.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 5 (2015), 2983-3008.

Dates
Received: 15 October 2014
Revised: 17 February 2015
Accepted: 20 February 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841039

Digital Object Identifier
doi:10.2140/agt.2015.15.2985

Mathematical Reviews number (MathSciNet)
MR3426700

Zentralblatt MATH identifier
1346.55004

Subjects
Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space
Secondary: 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX}

Keywords
Lusternik–Schnirelmann category lens spaces inessential manifolds ko-theory

Citation

Dranishnikov, Alexander N. The LS category of the product of lens spaces. Algebr. Geom. Topol. 15 (2015), no. 5, 2983--3008. doi:10.2140/agt.2015.15.2985. https://projecteuclid.org/euclid.agt/1510841039


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