Smooth manifolds with infinite fundamental group admitting no real\n projective structure

2018/11/22 by Hatice Çoban, Çoban, Hatice
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1811.09137

openalex publication_date 2018/11/22 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

It is an important question whether it is possible to put a geometry on a\ngiven manifold or not. It is well known that any simply connected closed\nmanifold admitting a real projective structure must be a sphere. Therefore, any\nsimply connected manifold M which is not a sphere (\dim M \≥ 4) does not\nadmit a real projective structure. Cooper and Goldman gave an example of a\n3-dimensional manifold not admitting a real projective structure and this is\nthe first known example. In this article, by generalizing their work we\nconstruct a manifold Mⁿ with the infinite fundamental group \ℤ₂\n\∗ \ℤ₂, for any n\≥ 4, admitting no real projective structure.\n

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