Skip to Main Content

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 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The space of framed functions
HTML articles powered by AMS MathViewer

by Kiyoshi Igusa PDF
Trans. Amer. Math. Soc. 301 (1987), 431-477 Request permission

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.
References
  • Jean Cerf, La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie, Inst. Hautes Études Sci. Publ. Math. 39 (1970), 5–173 (French). MR 292089
    • J. Finney, The invasion of the body snatchers, Dell, New York, 1978.
  • A. N. Godwin, Three dimensional pictures for Thom’s parabolic umbilic, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 117–138. MR 407885
  • Morris W. Hirsch, Differential topology, Graduate Texts in Mathematics, No. 33, Springer-Verlag, New York-Heidelberg, 1976. MR 0448362
    • K. Igusa, The ${\text {W}}{{\text {h}}_3}(\pi )$ obstruction for pseudoisotopy, Thesis, Princeton Univ., 1979.
  • Kiyoshi Igusa, Higher singularities of smooth functions are unnecessary, Ann. of Math. (2) 119 (1984), no. 1, 1–58. MR 736559, DOI 10.2307/2006962
  • Kiyoshi Igusa, On the homotopy type of the space of generalized Morse functions, Topology 23 (1984), no. 2, 245–256. MR 744854, DOI 10.1016/0040-9383(84)90043-0
    • —, The stability theorem for pseudoisotopies (in preparation).
  • Friedhelm Waldhausen, Algebraic $K$-theory of topological spaces. I, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 35–60. MR 520492
Similar Articles
Additional 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