Building planar polygon spaces from the projective braid arrangement
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Navnath Daundkar
Abstract
The moduli space of planar polygons with generic side lengths is a smooth, closed manifold. It is known that these manifolds contain the moduli space of distinct points on the real projective line as an open dense subset. Kapranov showed that the real points of the Deligne–Mumford–Knudson compactification can be obtained from the projective Coxeter complex of type 𝐴 (equivalently, the projective braid arrangement) by iteratively blowing up along the minimal building set. In this paper, we show that these planar polygon spaces can also be obtained from the projective Coxeter complex of type 𝐴 by performing an iterative cellular surgery along a subcollection of the minimal building set. Interestingly, this subcollection is determined by the combinatorial data associated with the length vector called the genetic code.
Funding source: Science and Engineering Research Board
Award Identifier / Grant number: MTR/2017/000239
Funding statement: P. Deshpande is partially supported by a grant from the Infosys Foundation. This project is also supported by the MATRICS grant MTR/2017/000239 funded by SERB.
Acknowledgements
The authors would like to thank the anonymous referee for the careful reading and important suggestions to improve the exposition of this article. The authors also thank Anurag Singh for useful discussions related to saturated chains of genetic codes.
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Communicated by: Clara Löh
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Articles in the same Issue
- Frontmatter
- The C*-algebra of the Boidol group
- Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order
- Positive rigs
- Torus bundles over lens spaces
- Topological amenability of semihypergroups
- On projections of the tails of a power
- Li–Yorke chaos for composition operators on Orlicz spaces
- A note on the post quantum-Sheffer polynomial sequences
- Finite rigid sets of the non-separating curve complex
- Building planar polygon spaces from the projective braid arrangement
- Octonionic monogenic and slice monogenic Hardy and Bergman spaces
- Transcendence on algebraic groups
- An explicit version of Bombieri’s log-free density estimate and Sárközy’s theorem for shifted primes
- The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras
- Joint distribution of the cokernels of random p-adic matrices II
Articles in the same Issue
- Frontmatter
- The C*-algebra of the Boidol group
- Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order
- Positive rigs
- Torus bundles over lens spaces
- Topological amenability of semihypergroups
- On projections of the tails of a power
- Li–Yorke chaos for composition operators on Orlicz spaces
- A note on the post quantum-Sheffer polynomial sequences
- Finite rigid sets of the non-separating curve complex
- Building planar polygon spaces from the projective braid arrangement
- Octonionic monogenic and slice monogenic Hardy and Bergman spaces
- Transcendence on algebraic groups
- An explicit version of Bombieri’s log-free density estimate and Sárközy’s theorem for shifted primes
- The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras
- Joint distribution of the cokernels of random p-adic matrices II
