2021/09/09 by Sheagan A. K. A. John, John, Sheagan A. K. A.
Mathematics · #54B10 #54C10 #54H25 #55M20 (Primary) #55N30 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2109.04057
openalex publication_date 2021/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For f,g:X\longrightarrow X continuous and commuting maps of a Hausdorff space, we investigate various conditions on X and on the pair (f,g) which provide existence of a coincidence value. We introduce generalized notions of the coincidence value property and use this added flexibility to determine how various coincidence properties of X are related to group actions on X and to coincidence properties of associated fibre bundles and adjunction spaces. We also present a sheaf theoretical approach to obtaining information concerning coincidence values through construction of an "almost constant" presheaf. In particular, we prove several partial results concerning the special cases where X is either a low dimensional dimensional sphere or the closed unit disk.