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1. Klaasse, R.L. Seiberg-Witten theory for symplectic manifolds.

Degree: 2013, Universiteit Utrecht

In this thesis we give an introduction to Seiberg-Witten gauge theory used to study compact oriented four-dimensional manifolds X. Seiberg-Witten theory uses a Spin c structure to create two vector bundles over X called the spinor bundle and determinant line bundle. One then considers the set of solutions to the Seiberg-Witten equations, which are expressed in terms of a section of the spinor bundle and a Dirac operator formed out of a connection on the determinant line bundle. After taking the quotient by an action of a U(1)-gauge group, one constructs an invariant by integrating cohomology classes over the resulting moduli space. In this thesis we show these Seiberg-Witten invariants can be used to find obstructions to the existence of a symplectic structure on X. Advisors/Committee Members: Cavalcanti, G.R..

Subjects/Keywords: Seiberg-Witten theory; four-manifolds; symplectic manifolds; Spin c structures; Dirac operators

…be unique. Many structures on the tangent bundle of a manifold can be expressed in terms of… …two different reductions of the structure group; • The reduction GL(n, C) < GL… …the next section, when we discuss the Spin(n) and Spinc (n) groups. Let… …principal U(1)-bundle over X can be identified with the space C ∞ (X; U(1)… …x28;X; E) (2.2.5) such that for all f ∈ C ∞ (X) and s ∈ Ω0 (… 

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APA (6th Edition):

Klaasse, R. L. (2013). Seiberg-Witten theory for symplectic manifolds. (Masters Thesis). Universiteit Utrecht. Retrieved from

Chicago Manual of Style (16th Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Masters Thesis, Universiteit Utrecht. Accessed February 26, 2021.

MLA Handbook (7th Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Web. 26 Feb 2021.


Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Internet] [Masters thesis]. Universiteit Utrecht; 2013. [cited 2021 Feb 26]. Available from:

Council of Science Editors:

Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Masters Thesis]. Universiteit Utrecht; 2013. Available from: