On the global monodromy of a Lefschetz fibration arising from the Fermat surface of degree 4
Yusuke Kuno
TL;DR
This paper provides a comprehensive description of the global monodromy for a Lefschetz fibration derived from the Fermat surface of degree 4, revealing new relations in the mapping class group of genus 3 surfaces.
Contribution
It offers the first complete description of the monodromy for this specific Lefschetz fibration and establishes a new positive relation among Dehn twists.
Findings
Complete monodromy description for the Fermat surface of degree 4
New positive relation among Dehn twists in genus 3 mapping class group
Insights into the topology of the associated Lefschetz fibration
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry