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2009

On manifolds with corners

Joyce, Dominic

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Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention.

The basic definitions in the subject are not agreed upon, there are several inequivalent definitions in use of manifolds with corners, of boundary, and of smooth map, depending on the applications in mind.
We present a theory of manifolds with corners which includes a new notion of smooth map f : X --> Y.
Compared to other definitions, our theory has the advantage of giving a category Man^c of manifolds with corners which is particularly well behaved as a category: it has products and direct products, boundaries behave in a functorial way, and there are simple conditions for the existence of fibre products X x_Z Y in Man^c.

On manifolds with corners · Around

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