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Models and string topology

Authors: García Pulido, Ana Lucía;

Models and string topology

Abstract

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

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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