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2018 Fundamental group of spaces of simple polygons
Ahtziri Gonzalez
Rocky Mountain J. Math. 48(6): 1871-1886 (2018). DOI: 10.1216/RMJ-2018-48-6-1871

Abstract

The space of shapes of $n$-gons with marked vertices can be identified with $\mathbb{C} \mathbb{P} ^{n-2}$. The space of shapes of $n$-gons without marked vertices is the quotient of $\mathbb{C} \mathbb{P} ^{n-2}$ by a cyclic group of order $n$ generated by the function which re-enumerates the vertices. In this paper, we prove that the subset corresponding to simple polygons, i.e., without self-intersections, in each case is open and has two homeomorphic, simply connected components.

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Ahtziri Gonzalez. "Fundamental group of spaces of simple polygons." Rocky Mountain J. Math. 48 (6) 1871 - 1886, 2018. https://doi.org/10.1216/RMJ-2018-48-6-1871

Information

Published: 2018
First available in Project Euclid: 24 November 2018

zbMATH: 06987229
MathSciNet: MR3879306
Digital Object Identifier: 10.1216/RMJ-2018-48-6-1871

Subjects:
Primary: 54B05, 55Q52

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 6 • 2018
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