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401-3533-DRL 3 Credits DR D-MATH

Generalized Nonpositive Curvature

Lecturers & Examiners: Prof. Dr. Urs Lang
Only for ZGSM (ETH D-MATH and UZH I-MATH) doctoral students. The latter need to register at myStudies and then send an email to with their name, course number and student ID. Please see
VVZ CR n/a

Last Updated: 2026-02-05 16:02:04

Abstract

CAT(0) spaces, Busemann convex spaces, metric spaces with convex geodesic bicombings; injective metric spaces and injective hulls; Gromov hyperbolicity, Helly graphs and Helly groups; fixed points, barycenter constructions, and applications.

Resources

Lecture Notes

Lectures notes will be provided.

Literature

- M. R. Bridson, A. Haefliger: Metric Spaces of Non-Positive Curvature, Springer 1999 - A. Papadopoulos: Metric Spaces, Convexity and Nonpositive Curvature, EMS 2005 - U. Lang: Injective hulls of certain discrete metric spaces and groups, J. Topol. Anal. 5 (2013), 297-331 - D. Descombes, U. Lang: Convex geodesic bicombings and hyperbolicity, Geom. Dedicata 177 (2015), 367-384 - J. Chalopin et al.: Weakly Modular Graphs and Nonpositive Curvature, Memoirs AMS 268 (2020), no. 1309 - J. Chalopin et al.: Helly groups, arXiv:2002.06895v2 [math.GR]

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture Generalized Nonpositive Curvature
  • Mon 10:15-12:00 (HG G 26.5)
  • Thu 13:15-14:00 (HG D 3.2)
3 h weekly

Offered In