Lefschetz fibrations with unbounded Euler class

Details Lefschetz fibrations with unbounded Euler class Lefschetz fibrations with unbounded Euler class

2001-09-03

arxiv.org/abs/math/0109011v4

Mathematics

Geometric Topology

8 pages, submitted to NYJM

Scientific paper

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.

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