Geography of surface bundles over surfaces
R. Inanc Baykur, Mustafa Korkmaz
TL;DR
This paper constructs symplectic surface bundles over surfaces with positive signatures for most pairs of fiber and base genera and also investigates the algebraic properties of certain mapping classes.
Contribution
It introduces new constructions of symplectic surface bundles with positive signatures and determines the commutator lengths of specific mapping classes.
Findings
Constructed symplectic surface bundles with positive signatures for nearly all genus pairs.
Determined the commutator lengths of several new mapping classes.
Provided new insights into the topology of surface bundles and mapping class groups.
Abstract
We construct symplectic surface bundles over surfaces with positive signatures for all but 18 possible pairs of fiber and base genera. Meanwhile, we determine the commutator lengths of a few new mapping classes.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology