2026-09-18T21:23:42Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/595862022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Haynes R. Miller.
Frankland, Martin
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2010-10-29T13:57:30Z
2010-10-29T13:57:30Z
2010
2010
http://hdl.handle.net/1721.1/59586
671249306
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.
162 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Quillen cohomology of pi-algebras and application to their realization by Martin Frankland.
Thesis
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