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Transactions of the American Mathematical Society

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

 

 

Simplexwise linear untangling


Author: David W. Henderson
Journal: Trans. Amer. Math. Soc. 298 (1986), 215-226
MSC: Primary 57Q35; Secondary 57M20, 57Q37
MathSciNet review: 857440
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0857440-3
Article copyright: © Copyright 1986 American Mathematical Society