Simplexwise linear untangling
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- by David W. Henderson PDF
- Trans. Amer. Math. Soc. 298 (1986), 215-226 Request permission
Abstract:
In this paper we show how to canonically untangle simplexwise linear spanning arcs of a convex $2$-cell. Specifically, we show that the space of such arcs is contractible. The main step in the contraction is a flow along the gradient field of an energy function. A $3$-dimensional version of this result would imply the Smale Conjecture—Hatcher Theorem.References
- Ethan D. Bloch, Robert Connelly, and David W. Henderson, The space of simplexwise linear homeomorphisms of a convex $2$-disk, Topology 23 (1984), no. 2, 161–175. MR 744848, DOI 10.1016/0040-9383(84)90037-5
- Robert Connelly, David W. Henderson, Chung Wu Ho, and Michael Starbird, On the problems related to linear homeomorphisms, embeddings, and isotopies, Continua, decompositions, manifolds (Austin, Tex., 1980) Univ. Texas Press, Austin, Tex., 1983, pp. 229–239. MR 711994
- A. E. Hatcher, Linearization in $3$-dimensional topology, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 463–468. MR 562642
- Allen E. Hatcher, A proof of the Smale conjecture, $\textrm {Diff}(S^{3})\simeq \textrm {O}(4)$, Ann. of Math. (2) 117 (1983), no. 3, 553–607. MR 701256, DOI 10.2307/2007035 D. Henderson, Relations between spaces of simplexwise linear and smooth embeddings, Preprint. M. Spivak, A comprehensive introduction to differential geometry, Vol. 1, Publish or Perish, Wilmington, Del., 1979.
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 298 (1986), 215-226
- MSC: Primary 57Q35; Secondary 57M20, 57Q37
- DOI: https://doi.org/10.1090/S0002-9947-1986-0857440-3
- MathSciNet review: 857440