First cohomology of pure mapping class groups of big genus one and zero\n surfaces

2019/04/23 by George Domat, Domat, George, Paul Plummer +2
Mathematics · #20F65 #57M07 #57S05 #Advanced Operator Algebra Research #Algebraic Geometry and Number Theory #Artificial intelligence #Biology #Botany #Class (philosophy) #Cohomology #Combinatorics #Computer science #Countable set #Discrete mathematics #FOS: Mathematics #Genus #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Group Theory (math.GR) #Homomorphism #Homotopy and Cohomology in Algebraic Topology #Mapping class group #Mathematics #Pure mathematics #Surface (topology) #Uncountable set #Zero (linguistics) #math.GR #math.GT #msc:20F65 #msc:57M07 #msc:57S05

paper · pdf · doi:10.48550/arxiv.1904.10565

14 pages, 3 figures

openalex publication_date 2019/04/23 · arxiv created 2020/02/03 · arxiv updated 2020/02/05 · openalex created_date 2022/07/29 · openalex updated_date 2026/08/04

Abstract

We prove that the first integral cohomology of pure mapping class groups of\ninfinite type genus one surfaces is trivial. For genus zero surfaces we prove\nthat not every homomorphism to \ℤ factors through a sphere with\nfinitely many punctures. In fact we get an uncountable family of such maps.\n

Citations

• THE MAPPING CLASS GROUP OF A DISK WITH INFINITELY MANY HOLES

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