The Euler class of infinite-type surface bundles

Mauricio Bustamante; Rita Jiménez Rolland; Israel Morales

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arXiv · 2509.21093

The Euler class of infinite-type surface bundles

Mauricio Bustamante·Rita Jiménez Rolland·Israel Morales

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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.

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Mauricio Bustamante, Rita Jiménez Rolland, Israel Morales. 2025-09-25. The Euler class of infinite-type surface bundles. https://arxiv.org/abs/2509.21093

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