Rocky Mountain Journal of Mathematics

Fundamental group of spaces of simple polygons

Ahtziri Gonzalez

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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.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 6 (2018), 1871-1886.

Dates
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1543028442

Digital Object Identifier
doi:10.1216/RMJ-2018-48-6-1871

Mathematical Reviews number (MathSciNet)
MR3879306

Zentralblatt MATH identifier
06987229

Subjects
Primary: 54B05: Subspaces 55Q52: Homotopy groups of special spaces

Keywords
Space of polygons simple polygons polygons without marked vertices

Citation

Gonzalez, Ahtziri. Fundamental group of spaces of simple polygons. Rocky Mountain J. Math. 48 (2018), no. 6, 1871--1886. doi:10.1216/RMJ-2018-48-6-1871. https://projecteuclid.org/euclid.rmjm/1543028442


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