Quillen cohomology of pi-algebras and application to their realization by Martin Frankland.

We use the obstruction theory of Blanc-Dwyer-Goerss to study the realization space of certain - algebras with 2 non-trivial groups. The main technical tool is a result on the Quillen cohomology of truncated -algebras, which is an instance of comparison map induced by an adjunction. We study in more generality the behavior of Quillen (co)homology with respect to adjunctions. As a first step toward applying the obstruction theory to 3-types, we develop methods to compute Quillen cohomology of 2-truncated -algebras via a generalization of group cohomology.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Frankland, Martin

Advisor dc:contributor.advisor

• Haynes R. Miller.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/59586

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/59586