An Equivariant Version of Hatcher's G/O Construction

TL;DR

This paper generalizes Hatcher's construction to explicitly generate the rational homotopy groups of the space of stable h-cobordisms for cyclic groups, aiding in classifying higher twisted torsion invariants.

Contribution

It introduces an equivariant version of Hatcher's G/O construction, providing explicit generators for rational homotopy groups in a new setting.

Findings

Explicit generators for rational homotopy groups of stable h-cobordisms

Generalization of Hatcher's construction to cyclic groups

Foundation for classifying higher twisted torsion invariants

Abstract

We explicitly construct generators of the rational homotopy groups of the space of stable h-cobordisms of the classifying space of a cyclic group of order n by generalizing a construction of Hatcher. This result will be used in a separate paper by the third author to classify axiomatic higher twisted torsion invariants.