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Bordered Heegaard Floer Homology, Satellites, and Decategorification

Tsvetelina Vaneva Petkova

Title:
Bordered Heegaard Floer Homology, Satellites, and Decategorification
Author(s):
Petkova, Tsvetelina Vaneva
Thesis Advisor(s):
Ozsvath, Peter S.
Date:
Type:
Dissertations
Department:
Mathematics
Permanent URL:
Notes:
Ph.D., Columbia University.
Abstract:
We use the methods of bordered Floer homology to provide a formula for both τ and HFK of certain satellite knots. In many cases, this formula determines the 4-ball genus of the satellite knot. In parallel, we explore the structural aspects of the bordered theory, developing the notion of an Euler characteristic for the modules associated to a bordered manifold. The Euler characteristic is an invariant of the underlying space, and shares many properties with the analogous invariants for closed 3-manifolds. We study the TQFT properties of this invariant corresponding to gluing, as well as its connections to sutured Floer homology. As one application, we show that the pairing theorem for bordered Floer homology categorifies the classical Alexander polynomial formula for satellites.
Subject(s):
Mathematics
Item views:
190
Metadata:
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