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Transformation Groups

, Volume 23, Issue 1, pp 149–183 | Cite as

ON THE GROMOV WIDTH OF POLYGON SPACES

Article

Abstract

For generic r = (r1,, rn) ∈ \( {\mathrm{\mathbb{R}}}_{+}^n \) the space ℳ(r) of n–gons in ℝ3 with edges of lengths r is a smooth, symplectic manifold. We investigate its Gromov width and prove that the expression 2π min {2r j , (∑ i ≠ j r i ) − r i |j = 1,  … , n} is the Gromov width of all (smooth) 5–gon spaces and of 6–gon spaces, under some condition on r\( {\mathrm{\mathbb{R}}}_{+}^6 \). The same formula constitutes a lower bound for all (smooth) spaces of 6–gons. Moreover, we prove that the Gromov width of ℳ(r) is given by the above expression when ℳ(r) is symplectomorphic to ℂℙ n − 3, for any n ≥ 4.

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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Departamento de MatemáticaPUC-RioRio de JaneiroBrazil
  2. 2.Mathematisches InstitutUniversität zu KölnKölnGermany

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