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Tour of bordered Floer theory.
Robert Lipshitz1, Peter S Ozsváth, Dylan P Thurston
1Department of Mathematics, Columbia University, New York, NY 10027, USA.
Summary
This survey introduces bordered Heegaard Floer homology, an extension of Heegaard Floer theory for 3-manifolds with boundaries. It details its construction and applications in topological quantum field theory.
Area of Science:
- Mathematics
- Topology
- Algebraic Topology
Background:
- Heegaard Floer theory is a topological quantum field theory.
- It assigns algebraic structures to 3-manifolds and 4-dimensional cobordisms.
Purpose of the Study:
- To explain the formal structure and construction of bordered Heegaard Floer homology.
- To demonstrate its utility in computing aspects of Heegaard Floer theory.
Main Methods:
- Formal definition of bordered Heegaard Floer homology.
- Exploration of its gluing properties as an extended TQFT.
Main Results:
- A comprehensive explanation of the construction of bordered Floer homology.
- Illustrations of its application in calculating invariants.
Conclusions:
- Bordered Heegaard Floer homology provides a powerful extension of Heegaard Floer theory.
- It offers new computational tools for topological quantum field theory.
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