Rudyak’s conjecture for low-dimensional simply connected manifolds
Fundamenta Mathematicae
MSC: Primary 55M30; Secondary 57R15, 57R65
DOI: 10.4064/fm251014-29-6
Published online: 29 October 2026
Abstract
Rudyak’s conjecture states that for any degree one map $f:M\to N$ between oriented closed manifolds there is the inequality $\operatorname{cat}(M)\ge \operatorname{cat}(N)$ for the Lusternik–Schnirelmann category. We prove this conjecture for $ n$-dimensional simply connected spin manifolds with $n\le 8$.
