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Topological complexity of planar polygon spaces with small genetic code

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Veröffentlicht/Copyright: 4. Juni 2016
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 29 Heft 2

Abstract

We determine lower bounds for the topological complexity of many planar polygon spaces mod isometry. With very few exceptions, the upper and lower bounds given by dimension and cohomology considerations differ by 1. This is true for 130 of the 134 generic 7-gon spaces. Our results apply to spaces of n-gons for all n, but primarily for those whose genetic codes, in the sense of Hausmann and Rodriguez, are moderately small.

Keywords: Topological complexity; planar polygon spaces
MSC 2010: 55M30; 58D29; 55R80

Communicated by Frederick R. Cohen

References

[1] Davis D. M., Real projective space as a space of planar polygons, Morfismos 19 (2015), 1–6. Suche in Google Scholar

[2] Davis D. M., www.lehigh.edu/~dmd1/mapleresults.pdf. Suche in Google Scholar

[3] Davis D. M., www.lehigh.edu/~dmd1/27cases.pdf. Suche in Google Scholar

[4] Farber M., Invitation to Topological Robotics, European Mathematcal Society, Zürich, 2008. 10.4171/054Suche in Google Scholar

[5] Hausmann J.-C. and Knutson A., The cohomology rings of polygon spaces, Ann. Inst. Fourier (Grenoble) 48 (1998), 281–321. 10.5802/aif.1619Suche in Google Scholar

[6] Hausmann J.-C. and Rodriguez E., The space of clouds in Euclidean space, Exp. Math. 13 (2004), 31–47. 10.1080/10586458.2004.10504521Suche in Google Scholar

[7] Hausmann J.-C. and Rodriguez E., www.unige.ch/math/folks/hausmann/polygones. Suche in Google Scholar

Received: 2015-12-29
Revised: 2016-1-23
Published Online: 2016-6-4
Published in Print: 2017-3-1

© 2017 by De Gruyter

Artikel in diesem Heft

  1. Frontmatter
  2. A note on the Hilali conjecture
  3. Finite groups have more conjugacy classes
  4. The gauge action, DG Lie algebras and identities for Bernoulli numbers
  5. Unitary embeddings of finite loop spaces
  6. Topological complexity of planar polygon spaces with small genetic code
  7. Numerical semigroups in a problem about cost-effective transport
  8. On the smallest simultaneous power nonresidue modulo a prime
  9. Decompositions of the higher order polars of plane branches
  10. A formula for the expected volume of the Wiener sausage with constant drift
  11. The slice spectral sequence for the C4 analog of real K-theory
  12. Incidences between points and generalized spheres over finite fields and related problems
  13. Mean values of the Witten L-function for SU(2)
  14. A direct computation of the cohomology of the braces operad
  15. Abelian varieties over finite fields as basic abelian varieties
https://doi.org/10.1515/forum-2016-0018
Schlagwörter für diesen Artikel
Topological complexity; planar polygon spaces

Artikel in diesem Heft

  1. Frontmatter
  2. A note on the Hilali conjecture
  3. Finite groups have more conjugacy classes
  4. The gauge action, DG Lie algebras and identities for Bernoulli numbers
  5. Unitary embeddings of finite loop spaces
  6. Topological complexity of planar polygon spaces with small genetic code
  7. Numerical semigroups in a problem about cost-effective transport
  8. On the smallest simultaneous power nonresidue modulo a prime
  9. Decompositions of the higher order polars of plane branches
  10. A formula for the expected volume of the Wiener sausage with constant drift
  11. The slice spectral sequence for the C4 analog of real K-theory
  12. Incidences between points and generalized spheres over finite fields and related problems
  13. Mean values of the Witten L-function for SU(2)
  14. A direct computation of the cohomology of the braces operad
  15. Abelian varieties over finite fields as basic abelian varieties
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