Topological Hermitian Cobordism

TL;DR

This paper extends methods used in Real cobordism to study the $RO(G)$-graded homotopy groups of a specific $ ext{Z}/2 imes ext{Z}/2$-equivariant spectrum called topological Hermitian cobordism, potentially aiding computations for other groups.

Contribution

It introduces a new approach for analyzing the homotopy groups of a non-complete $ ext{Z}/2 imes ext{Z}/2$-equivariant spectrum, expanding tools for equivariant stable homotopy theory.

Findings

Developed methods for $RO(G)$-graded homotopy groups of topological Hermitian cobordism.

Demonstrated potential applicability to other $G$-equivariant spectra with $G eq ext{Z}/2$.

Extended previous techniques used in Real cobordism to a broader class of equivariant spectra.

Abstract

Extending our method for investigating Real cobordism (which was recently used by Hill, Hopkins and Ravenel in their solution of the Kervaire invariant 1 problem), we investigate the $RO(G)$-graded homotopy groups of a (non-complete) $\Z/2\times \Z/2$-equivariant spectrum called topological Hermitian cobordism. The methods of this paper may be useful in computing the homotopy groups of other $G$-equivariant spectra where $G\neq \Z/2$.