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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The space of framed functions
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by Kiyoshi Igusa
Trans. Amer. Math. Soc. 301 (1987), 431-477
DOI: https://doi.org/10.1090/S0002-9947-1987-0882699-7
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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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Bibliographic Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 301 (1987), 431-477
  • MSC: Primary 57R65; Secondary 57R45, 57R70, 58C27
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0882699-7
  • MathSciNet review: 882699