The Euler class of infinite-type surface bundles

2025/09/25 by Bustamante, Mauricio, Rolland, Rita Jiménez, Morales, Israel
#55R40 #57K20 #57R20 #57R22 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2509.21093

Abstract

We study the Euler class of smooth orientable infinite-type surface bundles with a section. For many such surfaces, we show that this cohomology class is nontrivial, and that the behavior of its powers depends on the genus and the type of ends. As an application, we extend Morita's non-lifting theorem to many infinite-type surfaces, including surfaces of infinite genus.

Citations

• Torsion at the Threshold for Mapping Class Groups
• Compact and finite-type support in the homology of big mapping class groups
• A Moduli Space of Marked Hyperbolic Structures for Big Surfaces
• Non-realizability of some big mapping class groups
• Normal subgroups of big mapping class groups
• Big pure mapping class groups are never perfect
• The Alexander method for infinite-type surfaces
• Improved homological stability for the mapping class group with integral or twisted coefficients
• Homotopy types of homeomorphism groups of noncompact 2-manifolds

Related

• Infinitesimal Torelli Theorem for regular surfaces with very ample canonical divisor
• Signature of surface bundles and bounded cohomology
• Flat bundles and commutator lengths
• Asymptotic properties of MMM-classes
• Indecomposable surface bundles over surfaces