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Nonlocally Linear Manifolds and Orbifolds

In: Proceedings of the International Congress of Mathematicians

Author

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  • Shmuel Weinberger

    (University of Pennsylvania, Mathematics Department)

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.

Suggested Citation

  • Shmuel Weinberger, 1995. "Nonlocally Linear Manifolds and Orbifolds," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 637-647, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_57
    DOI: 10.1007/978-3-0348-9078-6_57
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