# The Cup-Length of Stiefel and Projective Stiefel Manifolds

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

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- mai 30, 2021
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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.