The space of framed functions

Igusa, Kiyoshi

doi:10.1090/S0002-9947-1987-0882699-7

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ISSN 1088-6850(online) ISSN 0002-9947(print)

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 and we show that the space of all framed functions on is $(\operatorname{dim} \,N - 1)$ -connected. A framed function on 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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