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 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 .
Citation
Alexander N Dranishnikov. "The LS category of the product of lens spaces." Algebr. Geom. Topol. 15 (5) 2983 - 3008, 2015. https://doi.org/10.2140/agt.2015.15.2985
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