Poincar\'e duality for $K$-theory of equivariant complex projective spaces

TL;DR

This paper explicitly formulates Poincaré duality in the equivariant $K$-theory of complex projective spaces, offering a novel perspective on $K$-theory orientation even in the trivial group case.

Contribution

It provides an explicit description of Poincaré duality in equivariant $K$-theory for complex projective spaces, including a new approach to $K$-theory orientation.

Findings

Explicit Poincaré duality formula for equivariant $K$-theory

New approach to $K$-theory orientation in the trivial group case

Enhanced understanding of equivariant complex projective spaces

Abstract

We make explicit Poincar\'{e} duality for the equivariant $K$-theory of equivariant complex projective spaces. The case of the trivial group provides a new approach to the $K$-theory orientation.