Maps of Degree 1 and Lusternik--Schnirelmann Category
Yuli Rudyak
TL;DR
This paper explores whether a degree 1 map between closed manifolds implies the Lusternik--Schnirelmann category of the target is not greater than that of the source, discussing related topological questions.
Contribution
It investigates the relationship between degree 1 maps and Lusternik--Schnirelmann categories, proposing new insights into their interplay in topology.
Findings
Discussion of conditions under which category inequalities hold
Identification of open questions in the relationship between degree 1 maps and categories
Proposed conjectures related to Lusternik--Schnirelmann category
Abstract
Given a map of degree 1 of closed manifolds. Is it true that the Lusternik--Schnirelmann category of the range of the map is not more that the category of the domain? We discuss this and some related questions.
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