Smooth manifolds with infinite fundamental group admitting no real projective structure

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Thesis Type: Doctorate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Faculty of Arts and Sciences, Department of Mathematics, Turkey

Approval Date: 2017

Student: HATİCE ÇOBAN

Supervisor: YILDIRAY OZAN

Abstract:

In this thesis, we construct smooth manifolds with the infinite fundamental group Z_2*Z_2, for any dimension n>=4, admitting no real projective structure. They are first examples of manifolds in higher dimensions with infinite fundamental group admitting no real projective structures. The motivation of our study is the related work of Cooper and Goldman. They proved that RP^3#RP^3 does not admit any real projective structure and this is the first known example in dimension 3.