Injective Simplicial Maps of the Arc Complex
نویسنده
چکیده
In this paper, we prove that each injective simplicial map of the arc complex of a compact, connected, orientable surface with nonempty boundary is induced by a homeomorphism of the surface. We deduce, from this result, that the group of automorphisms of the arc complex is naturally isomorphic to the extended mapping class group of the surface, provided the surface is not a disc, an annulus, a pair of pants, or a torus with one hole. We also show, for each of these special exceptions, that the group of automorphisms of the arc complex is naturally isomorphic to the quotient of the extended mapping class group of the surface by its center.
منابع مشابه
An introduction to simplicial sets
This is an elementary introduction to simplicial sets, which are generalizations of ∆-complexes from algebraic topology. The theory of simplicial sets provides a way to express homotopy and homology without requiring topology. This paper is meant to be accessible to anyone who has had experience with algebraic topology and has at least basic knowledge of category theory. An important part of si...
متن کاملInvariance of the barycentric subdivision of a simplicial complex
In this paper we prove that a simplicial complex is determined uniquely up to isomorphism by its barycentric subdivision as well as its comparability graph. We also put together several algebraic, combinatorial and topological invariants of simplicial complexes.
متن کاملVertex Decomposable Simplicial Complexes Associated to Path Graphs
Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...
متن کاملCohen-Macaulay-ness in codimension for simplicial complexes and expansion functor
In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.
متن کاملInjective Maps between Flip Graphs
We prove that every injective simplicial map F(S) → F(S′) between flip graphs is induced by a subsurface inclusion S → S′, except in finitely many cases. This extends a result of Korkmaz–Papadopoulos which asserts that every automorphism of the flip graph of a surface without boundary is induced by a surface homeomorphism.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008