On the equivariant cohomology of rotation groups and Stiefel manifolds

TL;DR

This paper computes the $RO(\mathbb{Z}/2)$-graded equivariant cohomology of rotation groups and Stiefel manifolds with specific involutions, advancing understanding of their topological and algebraic structures.

Contribution

It provides explicit calculations of equivariant cohomology for rotation groups and Stiefel manifolds under certain involutions, a novel contribution in equivariant topology.

Findings

Explicit $RO(\mathbb{Z}/2)$-graded cohomology computations

New insights into involution effects on topological spaces

Enhanced understanding of equivariant structures in geometry

Abstract

In this paper, we compute the $RO(\mathbb{Z}/2)$-graded equivariant cohomology of rotation groups and Stiefel manifolds with particular involutions.