Protocorks and monopole Floer homology
File(s)
Author(s)
Ladu, Roberto
Type
Thesis
Abstract
We introduce and study a class of compact 4-manifolds with boundary that we call protocorks. Any exotic pair of simply connected closed 4-manifolds is related by a protocork twist, moreover, any cork is supported by a protocork. We prove a theorem on the relative Seiberg-Witten invariants of a protocork before and after twisting and a splitting theorem
on the Floer homology of protocork boundaries.
As a corollary we improve a theorem by Morgan and Szab\'{o} regarding the variation of Seiberg-Witten invariants with an upper bound which depends only on the topology of the data. Moreover we show that for any cork, only the reduced Floer homology of its boundary contributes to the variation of the Seiberg-Witten invariants after a cork twist.
on the Floer homology of protocork boundaries.
As a corollary we improve a theorem by Morgan and Szab\'{o} regarding the variation of Seiberg-Witten invariants with an upper bound which depends only on the topology of the data. Moreover we show that for any cork, only the reduced Floer homology of its boundary contributes to the variation of the Seiberg-Witten invariants after a cork twist.
Version
Open Access
Date Issued
2022-09
Date Awarded
2022-12
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Sivek, Steven
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)