2008/12/26 by Jung Hoon Lee, Lee, Jung Hoon
Mathematics · #57M50 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M50 #msc:57N10
paper · pdf · doi:10.48550/arxiv.0812.4650
9 pages, 5 figures
arxiv created 2008/12/26 · arxiv updated 2009/12/01
We consider a Heegaard splitting M=H1 ∪S H2 of a 3-manifold M having an essential disk D in H1 and an essential surface F in H2 with |D ∩ F|=1. (We require that boundary of F is in S when H2 is a compressionbody with non-empty "minus" boundary.) Let F be a genus g surface with n boundary components. From S, we obtain a genus g(S)+2g+n-2 Heegaard splitting M=H'1 ∪S' H'2 by cutting H2 along F and attaching F × [0,1] to H1. As an application, by using a theorem due to Casson and Gordon, we give examples of 3-manifolds having two Heegaard splittings of distinct genera where one of the two Heegaard splittings is a strongly irreducible non-minimal genus splitting and it is obtained from the other by the above construction.