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The Space of Framed Functions is Contractible

In: Essays in Mathematics and its Applications

Author

Listed:
  • Y. M. Eliashberg

    (Stanford University)

  • N. M. Mishachev

    (Lipetsk Technical University)

Abstract

According to Igusa (Ann Math 119:1–58, 1984) a generalized Morse function on M is a smooth function $$M \rightarrow \mathbb{R}$$ with only Morse and birth-death singularities and a framed function on M is a generalized Morse function with an additional structure: a framing of the negative eigenspace at each critical point of f. In (Igusa, Trans Am Math Soc 301(2):431–477, 1987) Igusa proved that the space of framed generalized Morse functions is $$(\dim \,M - 1)$$ -connected. Lurie gave in (arXiv:0905.0465) an algebraic topological proof that the space of framed functions is contractible. In this paper we give a geometric proof of Igusa-Lurie’s theorem using methods of our paper (Eliashberg and Mishachev, Topology 39:711–732, 2000).

Suggested Citation

  • Y. M. Eliashberg & N. M. Mishachev, 2012. "The Space of Framed Functions is Contractible," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Essays in Mathematics and its Applications, edition 127, pages 81-109, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-28821-0_5
    DOI: 10.1007/978-3-642-28821-0_5
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