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Positive scalar curvature . . .
, 2005
"... We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension2 surgery technique which removes singular strata from fixed point free S¹manifolds while preserving equivariant ..."
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We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension2 surgery technique which removes singular strata from fixed point free S¹manifolds while preserving equivariant
Positive Scalar Curvature . . .
 PROC. AMER. MATH. SOC
"... The statement often called the GromovLawsonRosenberg Conjecture asserts that a manifold with finite fundamental group should admit a metric of positive scalar curvature except when the KO# valued index of some Dirac operator with coe#cients in a flat bundle is nonzero. We prove spin and orie ..."
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The statement often called the GromovLawsonRosenberg Conjecture asserts that a manifold with finite fundamental group should admit a metric of positive scalar curvature except when the KO# valued index of some Dirac operator with coe#cients in a flat bundle is nonzero. We prove spin
Symplectic fillings and positive scalar curvature
, 1998
"... Let X be a 4–manifold with contact boundary. We prove that the monopole invariants of X introduced by Kronheimer and Mrowka vanish under the following assumptions: (i) a connected component of the boundary of X carries a metric with positive scalar curvature and (ii) either b + 2 (X)> 0 or the bo ..."
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Cited by 30 (10 self)
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Let X be a 4–manifold with contact boundary. We prove that the monopole invariants of X introduced by Kronheimer and Mrowka vanish under the following assumptions: (i) a connected component of the boundary of X carries a metric with positive scalar curvature and (ii) either b + 2 (X)> 0
The space of metrics of positive scalar curvature
"... ABSTRACT. We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements in higher homotopy and homology groups of these spaces, which, in contrast to previous approaches, are of infinite order and survi ..."
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Cited by 8 (1 self)
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ABSTRACT. We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements in higher homotopy and homology groups of these spaces, which, in contrast to previous approaches, are of infinite order
POSITIVE SCALAR CURVATURE AND MINIMAL HYPERSURFACES
, 2003
"... Abstract. We show that the minimal hypersurface method of Schoen and Yau can be used for the “quantitative ” study of positive scalar curvature. More precisely, we show that if a manifold admits a metric g with sg> T  or sg> W , where sg is the scalar curvature of of g, T any 2tensor on M ..."
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Abstract. We show that the minimal hypersurface method of Schoen and Yau can be used for the “quantitative ” study of positive scalar curvature. More precisely, we show that if a manifold admits a metric g with sg> T  or sg> W , where sg is the scalar curvature of of g, T any 2tensor
SINGULAR LIMIT LAMINATIONS, MORSE INDEX, AND POSITIVE SCALAR CURVATURE
, 2002
"... index, and positive scalar curvature ..."
On higher etainvariants and metrics of positive scalar curvature
 K Theory 24:4 (2001), 341–359. MR 2002k:58051 Zbl 1010.58019
"... Abstract. Let N be a closed connected spin manifold admitting one metric of positive scalar curvature. In this paper we use the higher etainvariant associated to the Dirac operator on N in order to distinguish metrics of positive scalar curvature on N. In particular, we give sufficient conditions, ..."
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Cited by 16 (7 self)
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Abstract. Let N be a closed connected spin manifold admitting one metric of positive scalar curvature. In this paper we use the higher etainvariant associated to the Dirac operator on N in order to distinguish metrics of positive scalar curvature on N. In particular, we give sufficient conditions
Metrics of Positive Scalar Curvature and Connections With Surgery
 Annals of Math. Studies
, 2001
"... this paper will be assumed to be smooth (C 1 ). For simplicity, we restrict attention to compact manifolds, although there are also plenty of interesting questions about complete metrics of positive scalar curvature on noncompact manifolds. At some points in the discussion, however, it will be ne ..."
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Cited by 45 (1 self)
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this paper will be assumed to be smooth (C 1 ). For simplicity, we restrict attention to compact manifolds, although there are also plenty of interesting questions about complete metrics of positive scalar curvature on noncompact manifolds. At some points in the discussion, however
The eta Invariant and Metrics of Positive Scalar Curvature
, 1995
"... We use the eta invariant to detect families of non bordant metrics of positive scalar curvature on spin manifolds with non trivial finite fundamental groups of odd dimension m ≥ 5. ..."
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Cited by 23 (4 self)
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We use the eta invariant to detect families of non bordant metrics of positive scalar curvature on spin manifolds with non trivial finite fundamental groups of odd dimension m ≥ 5.
Results 1  10
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346,908