Lefschetz fibrations with unbounded Euler class

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We investigate the bounded cohomology of Lefschetz fibrations. If a Lefschetz fibration has regular fiber of genus at least 2 and it has at least two distinct vanishing cycles, we show that its Euler class is not bounded. As a consequence, we exclude the existence of negatively curved metrics on Lefschetz fibrations with more than one singular fiber.
8 pages, submitted to NYJM

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Geometric Topology, Algebraic Topology, Symplectic Geometry, 57N65

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http://salesiana.dossiersoluciones.com/handle/123456789/62131

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0109011
 http://arxiv.org/abs/math/0109011

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arXiv