A geometric description of the homology of surface bundles

2016/03/24 by Caterina Campagnolo, Campagnolo, Caterina
Mathematics · #57M50 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M50

paper · pdf · doi:10.48550/arxiv.1603.07639

9 pages, 1 figure

openalex publication_date 2016/03/24 · arxiv created 2016/05/11 · arxiv updated 2016/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We replace the wrong theorem of the previous version by some observations on the homology of surface bundles and explain why our previous strategy failed.

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