Geodesic
The LS category of the product of lens spaces
Dranishnikov, Alexander N1
1Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL 32611-8105, USA
Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2983-3008
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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 > n∕2. 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.

DOI : 10.2140/agt.2015.15.2985
Classification : 55M30, 55N15
Keywords: Lusternik–Schnirelmann category, lens spaces, inessential manifolds, ko-theory

Dranishnikov, Alexander N  1

1 Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL 32611-8105, USA 
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Dranishnikov, Alexander N. The LS category of the product of lens spaces. Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2983-3008. doi: 10.2140/agt.2015.15.2985

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