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

• Main Author: Frankland, Martin
• Other Authors: Haynes R. Miller.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2010
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/59586

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. === This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. === Cataloged from student-submitted PDF version of thesis. === Includes bibliographical references (p. 161-162). === 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. === Ph.D.