2021/11/23 by Daundkar, Navnath, Deshpande, Priyavrat, Goyal, Shuchita +1
#55M30 #55P15 #57R42 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2111.12033
The moduli space of planar polygons with generic side lengths is a closed, smooth manifold. Mapping a polygon to its reflected image across the X-axis defines a fixed-point-free involution on these moduli spaces, making them into free ℤ2-spaces. There are some important numerical parameters associated with free ℤ2-spaces, like index and coindex. In this paper, we compute these parameters for some moduli spaces of polygons. We also determine for which of these spaces a generalized version of the Borsuk-Ulam theorem hold. Moreover, we obtain a formula for the Stiefel-Whitney height in terms of the the genetic code, a combinatorial data associated with side lengths.