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Topological complexity of spatial polygon spaces


Author: Donald M. Davis
Journal: Proc. Amer. Math. Soc. 144 (2016), 3643-3645
MSC (2010): Primary 55M30, 58D29, 55R80
Published electronically: February 1, 2016
MathSciNet review: 3503733
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Abstract: Let $ \overline {\ell }=(\ell _1,\ldots ,\ell _n)$ be an $ n$-tuple of positive real numbers, and let $ N(\overline {\ell })$ denote the space of equivalence classes of oriented $ n$-gons in $ \mathbb{R}^3$ with consecutive sides of lengths $ \ell _1,\ldots ,\ell _n$, identified under translation and rotation of $ \mathbb{R}^3$. Using known results about the integral cohomology ring, we prove that its topological complexity satisfies $ \operatorname {TC}(N(\overline {\ell }))= 2n-5$, provided that $ N(\overline {\ell })$ is nonempty and contains no straight-line polygons.


References [Enhancements On Off] (What's this?)

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Additional Information

Donald M. Davis
Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Email: dmd1@lehigh.edu

DOI: https://doi.org/10.1090/proc/12998
Keywords: Topological complexity, spatial polygon spaces
Received by editor(s): July 9, 2015
Received by editor(s) in revised form: October 8, 2015
Published electronically: February 1, 2016
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2016 American Mathematical Society