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
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
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