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2008-05-18T19:34:47Z

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Vipul: New page: ==Definition== Suppose $M_1, M_2, P$ are differential manifolds, and $f_1:M_1 \to P, f_2:M_2 \to P$ are smooth maps. Then, a smooth cobordism from $f_1<...$

2008-02-28T02:08:14Z

New page: ==Definition== Suppose <math>M_1, M_2, P</math> are differential manifolds, and <math>f_1:M_1 \to P, f_2:M_2 \to P</math> are smooth maps. Then, a smooth cobordism from <math>f_1<...

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==Definition==

Suppose <math>M_1, M_2, P</math> are [[differential manifold]]s, and <math>f_1:M_1 \to P, f_2:M_2 \to P</math> are [[smooth map]]s. Then, a smooth cobordism from <math>f_1</math> to <math>f_2</math> is the following data:

* A [[smooth cobordism]] from <math>M_1</math> to <math>M_2</math> i.e. a [[manifold with boundary]] <math>(N, \partial N)</math> with a diffeomorphism <math>M_1 \sqcup M_2 \to \partial N</math>
* A [[smooth map]] <math>F:N \to P</math> such that the composite of <math>F</math> with the inclusions of <math>M_1, M_2</math> are respectively the maps <math>f_1, f_2</math>

Note that we may sometimes fix the cobordism between <math>M_1</math> and <math>M_2</math>, and ask whether we can ''fill in'' a function <math>F</math> for the particular cobordism.

Cobordism of smooth maps - Revision history

Vipul: 1 revision

Vipul: New page: ==Definition== Suppose M_1, M_2, P are differential manifolds, and f_1:M_1 \to P, f_2:M_2 \to P are smooth maps. Then, a smooth cobordism from f_1<...

Vipul: New page: ==Definition== Suppose $M_1, M_2, P$ are differential manifolds, and $f_1:M_1 \to P, f_2:M_2 \to P$ are smooth maps. Then, a smooth cobordism from $f_1<...$