2026-09-21T20:43:33Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/836942022-01-13T07:54:04Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Haynes R. Miller.
Horel, Geoffroy (Geoffroy Jean)
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2014-01-09T19:45:41Z
2014-01-09T19:45:41Z
2013
http://hdl.handle.net/1721.1/83694
864145165
Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 117-120).
In this thesis, we describe a general theory of modules over an algebra over an operad. We also study functors between categories of modules. Specializing to the operad [epsilon]d of little d-dimensional disks, we show that each (d - 1) manifold gives rise to a theory of modules over [epsilon]d-algebras and each bordism gives rise to a functor from the category defined by its incoming boundary to the category defined by its outgoing boundary. Then, we describe a geometric construction of the homomorphisms objects in these categories of modules inspired by factorization homology (also called chiral homology). A particular case of this construction is higher Hochschild cohomology or Hochschild cohomology of Ed-algebras. We compute the higher Hochschild cohomology of the Lubin-Tate ring spectrum and prove a generalization of a theorem of Kontsevich and Soibelman about the action of higher Hochschild cohomology on factorization homology.
by Geoffroy Horel.
Ph.D.
120 pages
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.
Operads, modules and higher Hochschild cohomology
Thesis
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<Abstract>In this thesis, we describe a general theory of modules over an algebra over an operad. We also study functors between categories of modules. Specializing to the operad [epsilon]d of little d-dimensional disks, we show that each (d - 1) manifold gives rise to a theory of modules over [epsilon]d-algebras and each bordism gives rise to a functor from the category defined by its incoming boundary to the category defined by its outgoing boundary. Then, we describe a geometric construction of the homomorphisms objects in these categories of modules inspired by factorization homology (also called chiral homology). A particular case of this construction is higher Hochschild cohomology or Hochschild cohomology of Ed-algebras. We compute the higher Hochschild cohomology of the Lubin-Tate ring spectrum and prove a generalization of a theorem of Kontsevich and Soibelman about the action of higher Hochschild cohomology on factorization homology.</Abstract>
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