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Collapsing and essential coverings
the Gromov-Hausdorff convergence Alexandrov spaces Betti numbers
2012/5/25
In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essenti...
Collapsing 4-manifolds under a lower curvature bound
collapsing Gromov-Hausdorff convergence Alexandrov spaces topology of 4-manifolds
2012/5/24
In this paper we describe the topology of 4-dimensional closed orientable Riemannian manifolds with a uniform lower bound of sectional curvature and with a uniform upper bound of diameter which collap...
Collapsing D-Branes in Calabi-Yau Moduli Space: I
Collapsing D-Branes Calabi-Yau Moduli Space
2010/11/2
We study the quantum volume of D-branes wrapped around various cycles in Calabi-Yau manifolds, as the manifold's moduli are varied. In particular, we focus on the behaviour of these D-branes near phas...