Sviben, Zvonimir: On the Monopole Map in Three Dimensions. 2018
Inhalt
- Introduction
- Preliminaries
- Notation and remarks
- Some identifications and conventions
- Scalar products and norms
- Clifford algebras and spin groups
- A different Clifford module structure on forms
- Dirac operator on forms
- The quadratic term
- The monopole map on 3-manifolds
- Assumptions and general context
- Seiberg-Witten equations on 3-manifolds
- Monopole map for closed 3-manifolds
- The refined Seiberg-Witten invariant for closed 3-manifolds
- New version of the monopole map
- Definition, assumptions and some notation
- Boundedness property
- Statement of the main result
- Renormalisation of the monopole map
- The monopole map on a 3-torus
- Notation and setup
- The Dirac operators
- The monopole map
- Sobolev spaces and elliptic operators
- Definition of Sobolev norms
- Stronger version of the elliptic estimate
- An equivalent definition of Sobolev norms
- Sobolev theorems
- Some facts from Hodge theory
- Some relations between Clifford and exterior algebras
- The connection Laplacian
- Endnotes
- Bibliography
- Notation
- Index