Lefschetz fibrations with unbounded Euler class
Geometric Topology
2007-05-23 v4 Algebraic Topology
Symplectic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/0109011,
title = {Lefschetz fibrations with unbounded Euler class},
author = {Thilo Kuessner},
journal= {arXiv preprint arXiv:math/0109011},
year = {2007}
}
Comments
8 pages, submitted to NYJM