English

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