2006/07/20 by Jesse Johnson, Johnson, Jesse
Mathematics · #57M #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M
paper · pdf · doi:10.48550/arxiv.math/0607513
30 pages, 8 figures
arxiv created 2006/07/20 · arxiv updated 2009/12/01
It is known that there are surface bundles of arbitrarily high genus which have genus two Heegaard splittings. The simplest examples are Seifert fibered spaces with the sphere as a base space, three exceptional fibers and which allow horizontal surfaces. We characterize the monodromy maps of all surface bundles with genus two Heegaard splittings and show that each is the result of integral Dehn surgery in one of these Seifert fibered spaces along loops where the Heegaard surface intersects a horizontal surface. (This type of surgery preserves both the bundle structure and the Heegaard splitting.)