A degree theorem for the simplicial closure of Auter space

2022/08/25 by Aygun, Juliet, Miller, Jeremy · 1 citation
#57K35 05E45 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2208.12358

Abstract

The degree of a based graph is the number of essential nonbasepoint 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.

Cited by

• An analogue of Rognes' connectivity conjecture for free groups

Related

• A combinatorial proof of the Degree Theorem in Auter space
• A Survey of Best Monotone Degree Conditions for Graph Properties
• On connected degree sequences
• An introduction to topological degree in Euclidean spaces
• A degree map on unimodular rows