On the global monodromy of a Lefschetz fibration arising from the Fermat surface of degree 4

Abstract

A complete description of the global monodromy of a Lefschetz fibration arising from the Fermat surface of degree 4 is given. As a by-product we get a positive relation among right hand Dehn twists in the mapping class group of a closed orientable surface of genus 3.

arXiv comment15 pages, 6 figures, 2 tables. The first version contained a crucial error in section 7, which leads to a wrong conclusion. To fix this error we need an additional data, that is Figure 7.2