Mathematics – Geometric Topology
Scientific paper
2008-12-26
Mathematics
Geometric Topology
9 pages, 5 figures
Scientific paper
We consider a Heegaard splitting M=H_1 \cup_S H_2 of a 3-manifold M having an essential disk D in H_1 and an essential surface F in H_2 with |D \cap F|=1. (We require that boundary of F is in S when H_2 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 \cup_S' H'_2 by cutting H_2 along F and attaching F \times [0,1] to H_1. 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.
No associations
LandOfFree
(Disk, Essential surface) pairs of Heegaard splittings that intersect in one point does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with (Disk, Essential surface) pairs of Heegaard splittings that intersect in one point, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and (Disk, Essential surface) pairs of Heegaard splittings that intersect in one point will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-295198