Manifold properties of planar polygon spaces

2018/04/05 by Donald M. Davis, Davis, Donald M.
Mathematics · #55R25 #57R20 #57R22 #57R25 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1804.01801

openalex publication_date 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the tangent bundle of a generic space of planar n-gons with specified side lengths, identified under isometry, plus a trivial line bundle is isomorphic to (n-2) times a canonical line bundle. We then discuss consequences for orientability, cobordism class, immersions, and parallelizability.

Related

• On the cohomology classes of planar polygon spaces
• The topology of spaces of polygons
• Topological complexity of some planar polygon spaces
• Real projective space as a space of planar polygons
• K-theory and immersions of spatial polygon spaces