Mathematics PhD Thesis Defense by Merve Cengiz

KOÇ UNIVERSITY

GRADUATE SCHOOL OF SCIENCES & ENGINEERING

MATHEMATICS

PhD THESIS DEFENSE BY MERVE CENGIZ

Title: Real Contact 3-Manifolds Through Surgery

Speaker: Merve Cengiz

Time: July 16, 2018, 11:00

Place: ENG 208

Koç University

Rumeli Feneri Yolu

Sariyer, Istanbul

Thesis Committee Members: 

Prof. Tolga Etgü (Advisor, Koç University)

Prof. Ferit Öztürk (Co-advisor, Boğaziçi University)

Assoc. Prof. Sinan Ünver (Koç University)

Prof. Teoman Turgut (Boğaziçi University)

Assoc. Prof. Çağrı Karakurt (Boğaziçi University)

Assoc. Prof.  Mehmetçik Pamuk (Middle East Technical University)

Abstract:

In this thesis, we study real contact 3-manifolds. A real 3-manifold is a smooth 3-manifold equipped with an orientation preserving involution with empty or 1-dimensional fixed point set. By a real contact manifold we mean a real manifold with an anti-symmetric contact structure. We prove that every real 3-manifold can be obtained from the standard real 3-sphere via equivariant surgeries and we give equivariant surgery descriptions for arbitrary real 3-manifolds. Then we define equivariant contact surgeries which allow one to extend the real contact structure to the surgered manifold. Via equivariant contact surgeries, we show that any real 3-manifold admits a real contact structure. We define two algorithms for constructing equivariant contact surgery diagrams and give examples to illustrate how our algorithms work. We determine that certain contact structures are real, obtaining them via equivariant contact surgeries.