Matches in SemOpenAlex for { <https://semopenalex.org/work/W265665615> ?p ?o ?g. }
- W265665615 endingPage "1804" @default.
- W265665615 startingPage "1731" @default.
- W265665615 abstract "In the context of CAT(0) cubical groups, we develop an analogue of the theory of curve complexes and subsurface projections. The role of the subsurfaces is played by a collection of convex subcomplexes called a emph{factor system}, and the role of the curve graph is played by the emph{contact graph}. There are a number of close parallels between the contact graph and the curve graph, including hyperbolicity, acylindricity of the action, the existence of hierarchy paths, and a Masur--Minsky-style distance formula. We then define a emph{hierarchically hyperbolic space}; the class of such spaces includes a wide class of cubical groups (including all virtually compact special groups) as well as mapping class groups and Teichm{u}ller space with any of the standard metrics. We deduce a number of results about these spaces, all of which are new for cubical or mapping class groups, and most of which are new for both. We show that the quasi-Lipschitz image from a ball in a nilpotent Lie group into a hierarchically hyperbolic space lies close to a product of hierarchy geodesics. We also prove a rank theorem for hierarchically hyperbolic spaces; this generalizes results of Behrstock--Minsky, Eskin--Masur--Rafi, Hamenst{a}dt, and Kleiner. We finally prove that each hierarchically hyperbolic group admits an acylindrical action on a hyperbolic space. This acylindricity result is new for cubical groups, in which case the hyperbolic space admitting the action is the contact graph; in the case of the mapping class group, this provides a new proof of a theorem of Bowditch." @default.
- W265665615 created "2016-06-24" @default.
- W265665615 creator A5009383506 @default.
- W265665615 creator A5035508502 @default.
- W265665615 creator A5056260500 @default.
- W265665615 date "2017-05-10" @default.
- W265665615 modified "2023-10-02" @default.
- W265665615 title "Hierarchically hyperbolic spaces, I: Curve complexes for cubical groups" @default.
- W265665615 cites W1496286207 @default.
- W265665615 cites W1496572257 @default.
- W265665615 cites W1649122824 @default.
- W265665615 cites W1709354625 @default.
- W265665615 cites W1963744099 @default.
- W265665615 cites W1965565198 @default.
- W265665615 cites W1972468321 @default.
- W265665615 cites W1972898102 @default.
- W265665615 cites W1976159947 @default.
- W265665615 cites W1989477049 @default.
- W265665615 cites W1993049165 @default.
- W265665615 cites W1997345328 @default.
- W265665615 cites W2011480326 @default.
- W265665615 cites W2016162729 @default.
- W265665615 cites W2020176431 @default.
- W265665615 cites W2026849456 @default.
- W265665615 cites W2033033894 @default.
- W265665615 cites W2033236171 @default.
- W265665615 cites W2035001592 @default.
- W265665615 cites W2037162327 @default.
- W265665615 cites W2039756040 @default.
- W265665615 cites W2049875683 @default.
- W265665615 cites W2051115580 @default.
- W265665615 cites W2057552663 @default.
- W265665615 cites W2060029831 @default.
- W265665615 cites W2061088591 @default.
- W265665615 cites W2062902318 @default.
- W265665615 cites W2074864316 @default.
- W265665615 cites W2085687370 @default.
- W265665615 cites W2092490925 @default.
- W265665615 cites W2094731111 @default.
- W265665615 cites W2104480106 @default.
- W265665615 cites W2105369534 @default.
- W265665615 cites W2108319291 @default.
- W265665615 cites W2123890277 @default.
- W265665615 cites W2143017204 @default.
- W265665615 cites W2148996685 @default.
- W265665615 cites W2152925334 @default.
- W265665615 cites W2158378607 @default.
- W265665615 cites W2314781788 @default.
- W265665615 cites W2315488227 @default.
- W265665615 cites W2616498484 @default.
- W265665615 cites W2788758712 @default.
- W265665615 cites W2963161312 @default.
- W265665615 cites W2963176827 @default.
- W265665615 cites W2963306825 @default.
- W265665615 cites W2963866382 @default.
- W265665615 cites W2963882168 @default.
- W265665615 cites W2964340618 @default.
- W265665615 cites W3036995422 @default.
- W265665615 cites W3099225457 @default.
- W265665615 cites W3100821931 @default.
- W265665615 cites W3105976821 @default.
- W265665615 cites W4205531361 @default.
- W265665615 cites W4236305466 @default.
- W265665615 cites W4237713313 @default.
- W265665615 cites W598301583 @default.
- W265665615 cites W8204747 @default.
- W265665615 doi "https://doi.org/10.2140/gt.2017.21.1731" @default.
- W265665615 hasPublicationYear "2017" @default.
- W265665615 type Work @default.
- W265665615 sameAs 265665615 @default.
- W265665615 citedByCount "72" @default.
- W265665615 countsByYear W2656656152013 @default.
- W265665615 countsByYear W2656656152014 @default.
- W265665615 countsByYear W2656656152015 @default.
- W265665615 countsByYear W2656656152016 @default.
- W265665615 countsByYear W2656656152017 @default.
- W265665615 countsByYear W2656656152018 @default.
- W265665615 countsByYear W2656656152019 @default.
- W265665615 countsByYear W2656656152020 @default.
- W265665615 countsByYear W2656656152021 @default.
- W265665615 countsByYear W2656656152022 @default.
- W265665615 countsByYear W2656656152023 @default.
- W265665615 crossrefType "journal-article" @default.
- W265665615 hasAuthorship W265665615A5009383506 @default.
- W265665615 hasAuthorship W265665615A5035508502 @default.
- W265665615 hasAuthorship W265665615A5056260500 @default.
- W265665615 hasBestOaLocation W2656656152 @default.
- W265665615 hasConcept C114614502 @default.
- W265665615 hasConcept C132525143 @default.
- W265665615 hasConcept C134306372 @default.
- W265665615 hasConcept C165818556 @default.
- W265665615 hasConcept C196278274 @default.
- W265665615 hasConcept C202444582 @default.
- W265665615 hasConcept C2524010 @default.
- W265665615 hasConcept C2776799497 @default.
- W265665615 hasConcept C33923547 @default.
- W265665615 hasConcept C83677898 @default.
- W265665615 hasConceptScore W265665615C114614502 @default.