an:02134781
Zbl 1062.57028
Kobayashi, Tsuyoshi; Qiu, Ruifeng; Rieck, Yo'av; Wang, Shicheng
Separating incompressible surfaces and stabilizations of Heegaard splittings
EN
Math. Proc. Camb. Philos. Soc. 137, No. 3, 633-643 (2004).
00111215
2004
j
57N10 57M50 57N16
Heegaard splitting; incompressible surface; amalgamation; stabilization
The authors develop an approach for the description of 3-manifolds containing closed separating incompressible surfaces of arbitrary large genus and find a ``simplest'' manifold of such sort. This result provides two applications.
1. For a closed orientable 3-manifold \(M\) and any positive integer \(m\) the surgery along any link \(L\) in \(M\) with at most \(2m+1\) components provides an irreducible 3-manifold containing \(m\) disjoint non-parallel separaring surfaces of arbitrarily high genus.
2. There exist 3-manifold \(M\) containing separating incompressible surfaces \(S_n\) of arbitrarily large genera \(g(S_n)\) such that the amalgamation of minimal Heegaard splittings of two resulting 3-manifolds cutting along \(S_n\) can be stabilized \(g(S_n)-3\) times to a minimal Heegaard splitting of \(M\).
Vassily O. Manturov (Moskva)