García Pulido, Ana Lucía (2012) Models and string topology. PhD thesis, University of Warwick.

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Abstract

This thesis concerns the study of string topology, a relatively new branch of
algebraic topology.
We begin with a survey of the background of string topology. In particular,
this includes a summary of the papers [4] by Chas and Sulivan, [15] by Jones and
[5] by Cohen and Jones that provide the background for the original work of this
thesis.
We then proceed to give a new e cient technique to do systematic computations
of the full structure of the string topology for a large family of manifolds.
For this, we rst use the results of Jones [15] and Cohen and Jones [5] to reduce
the problem to calculating Hochschild homology and cohomology. Secondly, we use
the concept of models to compute Hochschild homology and cohomology and obtain
some further Hochschild structure. Thus, most of this work is devoted to developing
this technique for calculating Hochschild homology and cohomology via models.
This research contributes to the area by providing the rst general and systematic
method of computing the full structure of string topology. In addition, we
give multiple, transparent examples of our new theory.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Algebraic topology, Mathematical models
Official Date:	December 2012
Dates:	Date Event December 2012 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Jones, J. D. S. (John D. S.)
Sponsors:	Consejo Nacional de Ciencia y Tecnología (Mexico) [Mexican Council for Science and Technology] (CONACYT)
Extent:	vi, 95 leaves : charts.
Language:	eng

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