Nonlocally Linear Manifolds and Orbifolds

Shmuel Weinberger
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Shmuel Weinberger: University of Pennsylvania, Mathematics Department

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 637-647 from Springer

Abstract: Abstract A topological manifold is, by definition, a Hausdorff topological space where each point has a neighborhood homeomorphic to Euclidean space. The geometrical topology of manifolds is a beautiful chapter in mathematics, and a great deal is now known about both the internal structure of manifolds (transversality, isotopy theorems, local contractibility, surgery theory, etc.) and their classification (cobordism theory, surgery theory, etc.). The subject that I would like to explore is the extension of this picture to a larger class of intrinsically interesting spaces (finite-dimensional ANR homology manifolds). Part of our exploration is motivated by an analogy between homology manifolds and orbifolds, that is, spaces that are modeled not on Euclidean space, but rather on the quotients of representation spaces by their finite linear actions.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_57

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