Operads, modules and higher Hochschild cohomology
Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2014
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| Online Access: | http://hdl.handle.net/1721.1/83694 |
| _version_ | 1826201898343989248 |
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| author | Horel, Geoffroy (Geoffroy Jean) |
| author2 | Haynes R. Miller. |
| author_facet | Haynes R. Miller. Horel, Geoffroy (Geoffroy Jean) |
| author_sort | Horel, Geoffroy (Geoffroy Jean) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013. |
| first_indexed | 2024-09-23T11:58:56Z |
| format | Thesis |
| id | mit-1721.1/83694 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T11:58:56Z |
| publishDate | 2014 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/836942019-04-11T10:40:55Z Operads, modules and higher Hochschild cohomology Horel, Geoffroy (Geoffroy Jean) Haynes R. Miller. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. 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. 2014-01-09T19:45:41Z 2014-01-09T19:45:41Z 2013 Thesis http://hdl.handle.net/1721.1/83694 864145165 eng 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. http://dspace.mit.edu/handle/1721.1/7582 120 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Horel, Geoffroy (Geoffroy Jean) Operads, modules and higher Hochschild cohomology |
| title | Operads, modules and higher Hochschild cohomology |
| title_full | Operads, modules and higher Hochschild cohomology |
| title_fullStr | Operads, modules and higher Hochschild cohomology |
| title_full_unstemmed | Operads, modules and higher Hochschild cohomology |
| title_short | Operads, modules and higher Hochschild cohomology |
| title_sort | operads modules and higher hochschild cohomology |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/83694 |
| work_keys_str_mv | AT horelgeoffroygeoffroyjean operadsmodulesandhigherhochschildcohomology |