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Bordered Heegaard Floer Homology and Graph Manifolds

Jonathan Hanselman

Title:
Bordered Heegaard Floer Homology and Graph Manifolds
Author(s):
Hanselman, Jonathan
Thesis Advisor(s):
Lipshitz, Robert
Date:
Type:
Dissertations
Department(s):
Mathematics
Persistent URL:
Notes:
Ph.D., Columbia University.
Abstract:
We use the techniques of bordered Heegaard Floer homology to investigate the Heegaard Floer homology of graph manifolds. Bordered Heegaard Floer homology allows us to split a graph manifold into pieces and perform computations for each piece separately. The resulting invariants can then be combined by a simple algebraic procedure to recover HFhat. Graph manifolds by definition decompose into pieces which are S¹-bundles over surfaces. This decomposition makes them particularly well suited to the divide-and-conquer techniques of bordered Heegaard Floer homology. In fact, the problem reduces to computing bordered Heegaard Floer invariants of just two pieces. The first invariant is the type D trimodule associated to the trivial S¹-bundle over the pair of pants
Subject(s):
Mathematics
Item views
443
Metadata:
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Suggested Citation:
Jonathan Hanselman, , Bordered Heegaard Floer Homology and Graph Manifolds, Columbia University Academic Commons, .

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