Homology, Homotopy and Applications

Volume 26 (2024)

Number 1

A degree theorem for the simplicial closure of Auter Space

Pages: 189 – 199

DOI: https://dx.doi.org/10.4310/HHA.2024.v26.n1.a13

Authors

Juliet Aygun (Department of Mathematics, Cornell University, Ithaca, New York, U.S.A.)

Jeremy Miller (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)

Abstract

The degree of a based graph is the number of essential non-basepoint vertices after generic perturbation. Hatcher–Vogtmann’s degree theorem states that the subcomplex of Auter Space of graphs of degree at most $d$ is $(d-1)$-connected. We extend the definition of degree to the simplicial closure of Auter Space and prove a version of Hatcher–Vogtmann’s result in this context.

Keywords

homology, homotopy

2010 Mathematics Subject Classification

20F28, 55U10

The full text of this article is unavailable through your IP address: 18.224.44.207

Received 8 December 2022

Received revised 30 March 2023

Accepted 18 April 2023

Published 1 May 2024