2020/09/23 by Gavrilovich Misha, Gavrilovich, Misha, Pimenov Konstantin +1
Mathematics · Physics and Astronomy · #54E15 #55U10 #Algebraic Topology (math.AT) #Algebraic and Geometric Analysis #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2009.11030
openalex publication_date 2020/09/23 · openalex created_date 2020/10/01 · openalex updated_date 2026/07/28
We interpret a construction of geometric realisation by [Besser], [Grayson], and [Drinfeld] of a simplicial set as constructing a space of maps from the interval to a simplicial set, in a certain formal sense, reminiscent of the Skorokhod space of semi-continuous functions; in particular, we show the geometric realisation functor factors through an endofunctor of a certain category. Our interpretation clarifies the explanation of [Drinfeld] "why geometric realization commutes with Cartesian products and why the geometric realization of a simplicial set [...] is equipped with an action of the group of orientation preserving homeomorphisms of the segment [0,1]".