Modul space for invariant solutions of Seiberg-Witten equations

Tez Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tez Danışmanı: Prof. Dr. Turgut Önder

Tezin Onay Tarihi: 1999

Tezin Dili: İngilizce

Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu

Özet:

ABSTRACT MODULI SPACE FOR INVARIANT SOLUTIONS OF SEIBERG-WITTEN EQUATIONS UĞUZ, MUHİDDİN Ph. D., Department of Mathematics Supervisor: Prof. Dr. Turgut Önder September 1999, 57 pages In this work we study the G-invariant solutions of the Seiberg-Witten equations when G is a cyclic group acting on a manifold M, preserving the metric and the orientation. G is assumed to have a lift to principle Spinc bundle which gives rise to Seiberg-Witten equations in question. It was shown that when the dimension b+ of the G-fixed points of harmonic two forms is positive, for a generic choice of an element in this fixed point set, the moduli space of invariant solutions of Seiberg-Witten equations is a compact, smooth and oriented manifold. In case b+ is zero, it was shown that there exist a unique singularity which has a compact neighborhood homeomorphic to a cone on a mcertain projective space. Using the latter case, a version of the theorem of Fintushel and Stern which gives a necessary condition for a Seifert homology 3-sphere occurs as the boundary of a negative definite four manifold whose first cohomology contains no 2-torsion, is proven.

Keywords: Equivariant Seiberg-Witten theory, Equivariant Seiberg-Witten moduli space, Pseudofree orbifold, Seifert homology 3-spheres.