A Combinatorial Substitute for the Degree Theorem in Auter Space

Details A Combinatorial Substitute for the Degree Theorem in Auter Space A Combinatorial Substitute for the Degree Theorem in Auter Space

2009-07-27

arxiv.org/abs/0907.4642v2

Mathematics

Group Theory

8 pages, fixed typesetting of an author's name, added a few clarifying sentences

Scientific paper

Auter space A_n is contractible. A. Hatcher and K. Vogtmann constructed a stratification of A_n into subspaces A_{n,k} such that A_{n,k} is k-connected. Their argument that A_{n,k} is (k-1)-connected, the Degree Theorem and its proof, is somewhat global in nature. Here we present a combinatorial substitute for the Degree Theorem that uses only local considerations to show that A_{n,k} is (k-1)-connected.

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