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Smooth manifolds with infinite fundamental group admitting no real projective structure

Tijdschriftbijdrage - Tijdschriftartikel

It is an important question whether it is possible to put a geometry on a given manifold or not. It is well known that any simply connected closed manifold admitting a real projective structure must be a sphere. Therefore, any simply connected manifold M which is not a sphere (dim M >= 4) does not admit a real projective structure. Cooper and Goldman gave an example of a 3-dimensional manifold not admitting a real projective structure and this is the first known example. In this article, by generalizing their work, we construct a manifold M-n with the infinite fundamental group Z(2)*Z(2), for any n >= 4, admitting no real projective structure.
Tijdschrift: Bulletin of the iranian mathematical society
ISSN: 1017-060X
Volume: 47
Pagina's: 335 - 363
Jaar van publicatie:2021
Trefwoorden:A1 Journal article
Toegankelijkheid:Open