An Upper Bound for the LS Category of Relative Sullivan Algebras

Organizers

陈伟彦、高鸿灏、黄意、林剑锋、邱宇、孙巍峰

Speaker

Jiawei Zhou 周嘉伟

Nanchang University

Time

Monday, 16:00 - 17:00

Oct. 27, 2025

Venue

C654, Shuangqing Complex Building

Zoom meeting ID: 405 416 0815

pw: 111111

An Upper Bound for the LS Category of Relative Sullivan Algebras

The Lusternik-Schnirelmann (LS) category is a numerical homotopy invariant of topological spaces, which measures the minimum number of contractible open sets needed to cover the space. For a fibration, an upper bound for its LS category can be given in terms of the categories of its base and fiber. In rational homotopy theory, certain fibrations are modeled by relative Sullivan algebras, for which an algebraic version of the LS category is defined. Felix, Halperin, and Thomas raised the question of whether the LS category of a relative Sullivan algebra is similarly bounded above by the categories of its base algebra and fiber algebra. In this talk, we provide a positive answer to this question.