Operads, modules and higher Hochschild cohomology

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2013

Author dc:creator

• Horel, Geoffroy (Geoffroy Jean)

Advisor dc:contributor.advisor

• Haynes R. Miller.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/83694

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/83694