Abstract
dc:description.abstractThe introduction of instanton Floer theory and Donaldson polynomial invariants in the 1980s revolutionised the study of low dimensional topology. Since then, many Floer theories have been introduced with different structural properties and qualitative features. One of these Floer theories, Heegaard Floer theory, is popular due to its computational ease and rich algebraic structure. One of the computational tools absent in other Floer theories is the integer surgery formula that computes Heegaard Floer homology of 3-manifolds obtained by surgery along knot(s) in them. This thesis establishes a new surgery formula in instanton Floer theory. The algebraic language to express this formula is that of the derived category of chain complexes. The first part of the thesis describes this surgery formula whose statement and proof are inspired by the Atiyah-Floer conjectures. The second part then contrasts with the Heegaard Floer analogue by showing that instanton and Heegaard Floer theory cannot agree over integers.
Degree
thesis:*- Name thesis:degree_name
- Doctoral
- Department dc:contributor.department
- Massachusetts Institute of Technology. Department of Mathematics
- Grantor dc:publisher
- Massachusetts Institute of Technology
- Year dc:date.issued
- 2024
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Bhat, Deeparaj
- Advisor dc:contributor.advisor
-
- Mrowka, Tomasz
Rights
dc:rights- Statement dc:rights
-
- In Copyright - Educational Use Permitted
- Copyright retained by author(s)
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- https://hdl.handle.net/1721.1/157113
- OAI identifier oai:identifier
- oai:dspace.mit.edu:1721.1/157113