Rudyak's conjecture for lower dimensional 1-connected manifolds

Rudyak's conjecture states that for any degree one map $f:M\to N$ between oriented closed manifolds there is the inequality $\cat (M)\ge \cat(N)$ for the Lusternik-Shnirelmann category. We prove the Rudyak's conjecture for $ n$-dimensional simply connected manifolds for $n\le 8$.

Publication Details

Journal
ArXiv.org
Published
2025-08-25
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

Rudyak's conjecture for lower dimensional 1-connected manifolds

ArXiv.org
Geochemistry and Geologic Mapping
article

Rudyak's conjecture for lower dimensional 1-connected manifolds

article en

Abstract

Rudyak's conjecture states that for any degree one map $f:M\to N$ between oriented closed manifolds there is the inequality $\cat (M)\ge \cat(N)$ for the Lusternik-Shnirelmann category. We prove the Rudyak's conjecture for $ n$-dimensional simply connected manifolds for $n\le 8$.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 61%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
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Rudyak's conjecture for lower dimensional 1-connected manifolds · ArXiv.org (2025) | TGRS Research Map | TGRS