From manifolds to invariants of En̳-algebras
Name
727152232-MIT.pdf
Description
Full printable version
Size
9.41 MB
Format
Adobe PDF
Checksum (MD5)
3eafa1b8a4469688825b1c9541f82876
Author(s)
Andrade, Ricardo (Ricardo Joel Abrantes Andrade)
Advisor(s)
Haynes R. Miller.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
This thesis is the first step in an investigation of an interesting class of invariants of En-algebras which generalize topological Hochschild homology. The main goal of this thesis is to simply give a definition of those invariants. We define PROPs EG, for G a structure group sitting over GL(n, R). Given a manifold with a (tangential) G-structure, we define functors EG[M]: (EG) 0 -+ Top constructed out of spaces of G-augmented embeddings of disjoint unions of euclidean spaces into M. These spaces are modifications to the usual spaces of embeddings of manifolds. Taking G - 1, El is equivalent to the n-little discs PROP, and El [M] is defined for any parallelized n-dimensional manifold M. The invariant we define for a Es-algebra A is morally defined by a derived coend TG(A; M) := EG[M] 9 A n EG for any n-manifold M with a G-structure. The case T' (A; Sl) recovers the topological Hochschild homology of an associative ring spectrum A. These invariants also appear in the work of Jacob Lurie and Paolo Salvatore, where they are involved in a sort of non-abelian Poincare duality.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
In title on title page, double underscored "n̳" appears as subscript. Cataloged from PDF version of thesis.
Includes bibliographical references (p. 241-242).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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