Abstract/Details

From manifolds to invariants of En-algebras

Andrade, Ricardo. Massachusetts Institute of Technology. ProQuest Dissertations Publishing, 2010. 0823483.

Abstract (summary)

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 [special characters omitted], for G a structure group sitting over GL (n, [special characters omitted]). Given a manifold with a (tangential) G-structure, we define functors [special characters omitted] 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, [special characters omitted] is equivalent to the n-little discs PROP, and [special characters omitted][M] is defined for any parallelized n-dimensional manifold M.

The invariant we define for a [special characters omitted]-algebra A is morally defined by a derived coend [special characters omitted] for any n-manifold M with a G-structure.

The case T¹ (A; S¹) 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 Poincaré duality. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Indexing (details)


Subject
Applied Mathematics;
Mathematics
Classification
0364: Applied Mathematics
0405: Mathematics
Identifier / keyword
Applied sciences; Pure sciences; En-algebras; G-structure; Group setting; Invariants; Manifolds
Title
From manifolds to invariants of En-algebras
Author
Andrade, Ricardo
Number of pages
0
Degree date
2010
School code
0753
Source
DAI-B 72/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
Advisor
Miller, Haynes R.
University/institution
Massachusetts Institute of Technology
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
0823483
ProQuest document ID
885231227
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/885231227