Skip navigation
Please use this identifier to cite or link to this item:
Title: Combinatorial Methods in Bordered Heegaard Floer Homology
Authors: Zhan, Bohua
Advisors: Szabo, Zoltan
Contributors: Mathematics Department
Keywords: Heegaard Floer homology
Low dimensional topology
Subjects: Mathematics
Issue Date: 2014
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis we give several combinatorial constructions and proofs in bordered Heegaard Floer homology. In the first part, we give an explicit description of a rank-1 model of CFAA(I), the type AA invariant associated to the identity diffeomorphism. This leads to a combinatorial proof of the quasi-invertibility of CFDD(I). In the second part, we use the newly constructed CFAA(I) to describe the type DA invariant CFDA(\tau) for any arcslide \tau. Using this, we give a combinatorial construction of HF(Y) for any 3-manifold Y, and prove that it is a 3-manifold invariant. Along the way, we prove combinatorially that bordered Floer theory gives a linear-categorical representation of the (strongly-based) mapping class groupoid. In the third part, we develop the theory of local type DA bimodules and extension by identity, and use it to give another construction of CFDA(\tau) for arcslides, which leads to a faster algorithm to compute HF for an arbitrary 3-manifold.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

Files in This Item:
File Description SizeFormat 
Zhan_princeton_0181D_10943.pdf867.67 kBAdobe PDFView/Download

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.