Following the work of Conant and Vogtmann on determining the homology of the group of outer automorphisms of a free group, a new nontrivial class in the rational homology of Outer space is established for the free group of rank eight. The methods started in [8] are heavily exploited and used to create a new graph complex called the space of good chord diagrams. This complex carries with it significant computational advantages in determining possible nontrivial homology classes.Next, we create a basepointed version of the Lie operad and explore some of it proper- ties. In particular, we prove a Kontsevich-type theorem that relates the Lie homology of a particular space to the cohomology of the group of automorphisms of the free group.
| Identifer | oai:union.ndltd.org:UTENN/oai:trace.tennessee.edu:utk_graddiss-2150 |
| Date | 01 May 2011 |
| Creators | Gray, Jonathan Nathan |
| Publisher | Trace: Tennessee Research and Creative Exchange |
| Source Sets | University of Tennessee Libraries |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Doctoral Dissertations |
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