Operads, modules and higher Hochschild cohomology
Name
864145165-MIT.pdf
Description
Full printable version
Size
4.85 MB
Format
Adobe PDF
Checksum (MD5)
b15005aaae623e4a6adbade46618da93
Author(s)
Horel, Geoffroy (Geoffroy Jean)
Advisor(s)
Haynes R. Miller.
Date Issued
2013
Publisher
Massachusetts Institute of Technology
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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