 

Robert McEwen and Matthew C. B. Zaremsky
A combinatorial proof of the Degree Theorem in Auter space view print


Published: 
March 4, 2014 
Keywords: 
Auter space, Degree Theorem, automorphisms of free groups 
Subject: 
Primary 20F65; Secondary 57M07, 20F28 


Abstract
We use discrete Morse theory to give a new proof of Hatcher and Vogtmann's Degree Theorem in Auter space A_{n}. There is a filtration of A_{n} into subspaces A_{n,k} using the degree of a graph, and the Degree Theorem says that each A_{n,k} is (k1)connected. This result is useful, for example to calculate stability bounds for the homology of Aut(F_{n}). The standard proof of the Degree Theorem is global in nature. Here we give a proof that only uses local considerations, and lends itself more readily to generalization.


Acknowledgements
The second named author gratefully acknowledges support from the SFB 701 of the DFG


Author information
Robert McEwen:
Ruckersville, VA 22968
mcewen.rob@gmail.com
Matthew C. B. Zaremsky:
Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902
zaremsky@math.binghamton.edu

