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The Global ETD Search service is a free service for researchers
to find electronic theses and dissertations. This service is
provided by the
Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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On the homology of automorphism groups of free groups.Gray, Jonathan Nathan 01 May 2011 (has links)
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.
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Semistable Graph Homology / Semistable Graph HomologyZúñiga, Javier 25 September 2017 (has links)
Using the orbicell decomposition of the Deligne-Mumford compactification of the moduli space of Riemann surfaces studied before by the author, a chain complex based on semistable ribbon graphs is constructed which is an extension of the Konsevich’s graph homology. / En este trabajo mediante la descomposicion orbicelular de la compacticacion de Deligne-Mumford del espacio de moduli de supercies de Riemann (estudiada antes por el autor) construimos un complejo basado en grafos de cinta semiestables, lo cual constituye una extension de la homologa de grafos de Kontsevich.
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