The Cup-Length of Stiefel and Projective Stiefel Manifolds

The Cup-Length of Stiefel and Projective Stiefel Manifolds

Július Korbaš, Renate Scheidler, Peter Zvengrowski – GJM, Volume 6, Issue 1 (2021), 27-34.

This paper discusses some generalities about cup-length of manifolds and then gives an explicit formula for the \mathbb Z_2-cup-length of the Stiefel manifolds V_{n,r}, as well as strong lower bounds for the \mathbb Z_2-cup-length of the projective Stiefel manifolds X_{n,r}, for all 1 \leq r\leq n-1. A simple formula relating the two cases is given.

We also show the consequences for the Lyusternik-Shnirel’man category, as well as a family of interesting number theoretical identities that arise from the V_{n,r} calculations.

Categories: Issue1

Milestones:

Received: June 5, 2020
Accepted: September 2020
Revised: March 25, 2021
Published online: May 29, 2021

Authors:

Július Korbaš
Department of Algebra and Geometry,
Faculty of Mathematics, Physics, and Informatics,
Comenius University, Mlynska dolina,
SK-842 48 Bratislava 4, Slovakia.

Renate Scheidler
Department of Mathematics and Statistics,
The University of Calgary, Calgary,
Alberta T2N 1N4, Canada.

Peter Zvengrowski
Department of Mathematics and Statistics,
The University of Calgary, Calgary,
Alberta T2N 1N4, Canada.

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