A Birman exact sequence for Aut(Fn)
| dc.citation.journalTitle | Advances in Mathematics | en_US |
| dc.citation.volumeNumber | 231 | en_US |
| dc.contributor.author | Day, Matthew | en_US |
| dc.contributor.author | Putman, Andrew | en_US |
| dc.date.accessioned | 2013-09-13T15:43:23Z | |
| dc.date.available | 2013-09-13T15:43:23Z | |
| dc.date.issued | 2012 | en_US |
| dc.description.abstract | The Birman exact sequence describes the effect on the mapping class group of a surface with boundary of gluing discs to the boundary components. We construct an analogous exact sequence for the automorphism group of a free group. For the mapping class group, the kernel of the Birman exact sequence is a surface braid group. We prove that in the context of the automorphism group of a free group, the natural kernel is finitely generated. However, it is not finitely presentable; indeed, we prove that its second rational homology group has infinite rank by constructing an explicit infinite collection of linearly independent abelian cycles. We also determine the abelianization of our kernel and build a simple infinite presentation for it. The key to many of our proofs are several new generalizations of the Johnson homomorphisms. | en_US |
| dc.embargo.terms | none | en_US |
| dc.identifier.citation | Day, Matthew and Putman, Andrew. "A Birman exact sequence for Aut(Fn)." <i>Advances in Mathematics,</i> 231, (2012) Elsevier: <a href="https://hdl.handle.net/1911/71894">https://hdl.handle.net/1911/71894</a>. | |
| dc.identifier.uri | https://hdl.handle.net/1911/71894 | |
| dc.language.iso | eng | en_US |
| dc.publisher | Elsevier | |
| dc.rights | This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier. | en_US |
| dc.title | A Birman exact sequence for Aut(Fn) | en_US |
| dc.type | Journal article | en_US |
| dc.type.dcmi | Text | en_US |
| dc.type.publication | post-print | en_US |