Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 5 (2015), 2983-3008.
The LS category of the product of lens spaces
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 with relatively prime and . We have computed for values , . It turns out that our computation supports the conjecture.
For spin manifolds we establish a criterion for the equality , which is a K–theoretic refinement of the Katz–Rudyak criterion for . We apply it to obtain the inequality for all odd and odd relatively prime and .
Algebr. Geom. Topol., Volume 15, Number 5 (2015), 2983-3008.
Received: 15 October 2014
Revised: 17 February 2015
Accepted: 20 February 2015
First available in Project Euclid: 16 November 2017
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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