Infinite topology of curve complexes and non-Poincare duality of Teichmueller modular groups

2007/07/29 by Nikolai V. Ivanov, Ivanov, Nikolai V., Lizhen Ji +1 · 1 citation
Mathematics · #20F38 #20J06 #30F60 #32G15 (Primary) #57M07 #57M99 (Secondary) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20F38 #msc:20J06 #msc:30F60 #msc:32G15 #msc:57M07 #msc:57M99

paper · pdf · doi:10.48550/arxiv.0707.4322

11 pages, no figures

arxiv created 2007/07/29 · openalex publication_date 2007/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we fill in a gap in the literature by proving that the Teichmueller modular groups (mapping class groups) are not Poincare duality groups and the complexes of curves of surfaces have infinite homotopy type (i.e. are not homotopy equivalent to a finite CW-complex).

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