Quillen cohomology of pi-algebras and application to their realization by Martin Frankland.
Massachusetts Institute of Technology. Dept. of Mathematics.
Haynes R. Miller.
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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.
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).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology