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Transactions of the American Mathematical Society

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The space of framed functions

Author: Kiyoshi Igusa
Journal: Trans. Amer. Math. Soc. 301 (1987), 431-477
MSC: Primary 57R65; Secondary 57R45, 57R70, 58C27
MathSciNet review: 882699
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Abstract: We define the notion of a ``framed function'' on a compact smooth manifold $ N$ and we show that the space of all framed functions on $ N$ is $ (\operatorname{dim} \,N - 1)$-connected. A framed function on $ N$ is essentially a smooth function $ N \to \mathbf{R}$ with only Morse and birth-death singularities together with certain additional structure.

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Keywords: Singularities, smooth manifolds, Morse functions, jet bundles, cell complexes
Article copyright: © Copyright 1987 American Mathematical Society