## Operads, modules and higher Hochschild cohomology

##### Author(s)

Horel, Geoffroy (Geoffroy Jean)
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##### Other Contributors

Massachusetts Institute of Technology. Department of Mathematics.

##### Advisor

Haynes R. Miller.

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Show full item record##### 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.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013. Cataloged from PDF version of thesis. Includes bibliographical references (pages 117-120).

##### Date issued

2013##### Department

Massachusetts Institute of Technology. Department of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.