Rudyak's conjecture for lower dimensional 1-connected manifolds

TL;DR

This paper proves Rudyak's conjecture for degree one maps between simply connected spin manifolds of dimension up to 8, establishing an inequality for their Lusternik-Shnirelmann categories.

Contribution

It extends the validity of Rudyak's conjecture to all simply connected spin manifolds of dimension up to 8.

Findings

Proves Rudyak's conjecture for n-dimensional simply connected spin manifolds with n ≤ 8.

Establishes the inequality cat(M) ≥ cat(N) for degree one maps in this class.

Confirms the conjecture in new low-dimensional cases.

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 spin manifolds for $n\le 8$.