NDLI: Hyperbolic rank and subexponential corank of metric spaces

Content Provider	Springer Nature Link
Author	Buyalo, S. Schroeder, V.
Copyright Year	2002
Abstract	We introduce a new quasi-isometry invariant corank X of a metric space X called subexponential corank. A metric space X has subexponential corank k if roughly speaking there exists a continuous map $ g : X \to T $ , T is a topological space, such that for each $ t \in T $ the set g -1(t) has subexponential growth rate in X and the topological dimension dimT = k is minimal among all such maps. Our main result is the inequality $ \mathrm{rank}_h\,X \le\,\mathrm{corank}\,X $ for a large class of metric spaces X including all locally compact Hadamard spaces, where rank h X is the maximal topological dimension of $ \partial_\infty Y $ among all CAT(—1) spaces Y quasi-isometrically embedded into X (the notion introduced by M. Gromov in a slightly stronger form). This proves several properties of rank h conjectured by Gromov, in particular, that any Riemannian symmetric space X of noncompact type possesses no quasi-isometric embedding $ H^n \to X $ of the standard hyperbolic space H n with $ n - 1 > \mathrm{dim}\,X - \mathrm{rank}\,X $ .
Starting Page	293
Ending Page	306
Page Count	14
File Format	PDF
ISSN	1016443X
Journal	Geometric and Functional Analysis
Volume Number	12
Issue Number	2
e-ISSN	14208970
Language	English
Publisher	Birkhäuser Verlag
Publisher Date	2002-06-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Analysis Geometry and Topology

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Hyperbolic rank and subexponential corank of metric spaces

Products of Hyperbolic Metric Spaces

A Characterization of Homogeneous Spaces with Positive Hyperbolic Rank

Corank and asymptotic filling-invariants for symmetric spaces

Bi-Lipschitz extension from boundaries of certain hyperbolic spaces

Least Area Planes in Gromov Hyperbolic 3-Spaces with Co-compact Metric

Isometry Groups of Proper Hyperbolic Spaces

Some Groups Having Only Elementary Actions on Metric Spaces with Hyperbolic Boundaries

Embeddings of Gromov hyperbolic spaces

Hyperbolic rank and subexponential corank of metric spaces

Similar Documents

Hyperbolic rank and subexponential corank of metric spaces

Products of Hyperbolic Metric Spaces

A Characterization of Homogeneous Spaces with Positive Hyperbolic Rank

Corank and asymptotic filling-invariants for symmetric spaces

Bi-Lipschitz extension from boundaries of certain hyperbolic spaces

Least Area Planes in Gromov Hyperbolic 3-Spaces with Co-compact Metric

Isometry Groups of Proper Hyperbolic Spaces

Some Groups Having Only Elementary Actions on Metric Spaces with Hyperbolic Boundaries

Embeddings of Gromov hyperbolic spaces

Hyperbolic rank and subexponential corank of metric spaces