An isovariant Blakers--Massey theorem

TL;DR

This paper develops foundational results in isovariant stable homotopy theory, including a Blakers--Massey theorem, a suspension notion, and a Freudenthal suspension theorem, advancing the understanding of equivariant maps that preserve isotropy groups.

Contribution

It introduces the first isovariant Blakers--Massey theorem, generalizes it to n-cubes, and establishes key suspension and Freudenthal theorems in the isovariant setting.

Findings

Proved an isovariant Blakers--Massey theorem.

Established an n-cubical generalization.

Defined a suspension in the isovariant category and proved a Freudenthal suspension theorem.

Abstract

An isovariant map is an equivariant map between $G$-spaces which strictly preserves isotropy groups. In this paper, we lay the groundwork for the study of isovariant stable homotopy theory. We prove an isovariant Blakers--Massey theorem and its $n$-cubical generalization, define a suitable notion of suspension (by a trivial representation sphere) in the isovariant category, and prove an isovariant Freudenthal suspension theorem.