Equivariant Algebraic Cobordism and Double Point Relations

TL;DR

This paper develops an equivariant algebraic cobordism theory for groups over fields of characteristic zero, extending double point relations, and provides explicit generators for finite abelian groups.

Contribution

It introduces a generalized double point relation-based equivariant algebraic cobordism theory and determines explicit generators for finite abelian groups.

Findings

Defined an equivariant algebraic cobordism theory for reductive and finite groups.

Proved basic properties and well-definedness of a fixed point map.

Explicitly described generators of the cobordism ring for finite abelian groups.

Abstract

For a reductive connected group or a finite group over a field of characteristic zero, we define an equivariant algebraic cobordism theory by a generalized version of the double point relation of Levine-Pandharipande. We prove basic properties and the well-definedness of a canonical fixed point map. We also find explicit generators of the algebraic cobordism ring of the point when the group is finite abelian.