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ON THE STRUCTURE OF THE FUNDAMENTAL GROUP OF MANIFOLDS WITH POSITIVE SCALAR CURVATURE
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 Title & Authors
ON THE STRUCTURE OF THE FUNDAMENTAL GROUP OF MANIFOLDS WITH POSITIVE SCALAR CURVATURE
Kim, Jin-Hong; Park, Han-Chul;
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 Abstract
The aim of this paper is to study the structure of the fundamental group of a closed oriented Riemannian manifold with positive scalar curvature. To be more precise, let M be a closed oriented Riemannian manifold of dimension n (4 n 7) with positive scalar curvature and non-trivial first Betti number, and let be non-trivial codimension one homology class in (M;). Then it is known as in [8] that there exists a closed embedded hypersurface of M representing of minimum volume, compared with all other closed hypersurfaces in the homology class. Our main result is to show that the fundamental group is always virtually free. In particular, this gives rise to a new obstruction to the existence of a metric of positive scalar curvature.
 Keywords
fundamental group;positive scalar curvature;
 Language
English
 Cited by
1.
ADDENDUM AND ERRATUM TO "ON THE STRUCTURE OF THE FUNDAMENTAL GROUP OF MANIFOLDS WITH POSITIVE SCALAR CURVATURE",;

대한수학회보, 2013. vol.50. 2, pp.537-542 crossref(new window)
1.
ADDENDUM AND ERRATUM TO "ON THE STRUCTURE OF THE FUNDAMENTAL GROUP OF MANIFOLDS WITH POSITIVE SCALAR CURVATURE", Bulletin of the Korean Mathematical Society, 2013, 50, 2, 537  crossref(new windwow)
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