Let M be a compact orientable irreducible 3-manifold, and F be an essential connected closed surface in M which cuts M into two manifolds M1 and M2. If Mi has a minimal Heegaard splitting Mi = Vi∪Hi Wi with d（H1） ...Let M be a compact orientable irreducible 3-manifold, and F be an essential connected closed surface in M which cuts M into two manifolds M1 and M2. If Mi has a minimal Heegaard splitting Mi = Vi∪Hi Wi with d（H1） ＋ d（H2） ≥ 2（g（M0 ＋ g（M2） - g（F）） ＋ 1, then g（M） = g（M1） ＋ g（M2） - g（F）.展开更多
A closed orientable Haken 3-manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation.Heegaard distanc...A closed orientable Haken 3-manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation.Heegaard distance introduced by Hempel is a useful index in studying Heegaard splitting. This paper studies the stabilization problem for the bilateral self-amalgamation, and proves that if the distance of bilateral selfamalgamation of a Heegaard splitting is at least 9, then it is unstabilized, weakly reducible and irreducible.展开更多
Let V ∪SW be a Heegaard splitting of M,such that αM = α-W = F1 ∪ F2 and g(S) = 2g(F1)= 2g(F2). Let V * ∪S*W * be the self-amalgamation of V ∪SW. We show if d(S) 3 then S* is not a topologically minimal surface.
基金Project supported by the National Natural Science Foundation of China(No.10625102)
文摘Let M be a compact orientable irreducible 3-manifold, and F be an essential connected closed surface in M which cuts M into two manifolds M1 and M2. If Mi has a minimal Heegaard splitting Mi = Vi∪Hi Wi with d（H1） ＋ d（H2） ≥ 2（g（M0 ＋ g（M2） - g（F）） ＋ 1, then g（M） = g（M1） ＋ g（M2） - g（F）.
基金supported by National Natural Science Foundation of China(Grant Nos.11271058 and 11371076)the Fundamental Research Funds for the Central Universities(Grant No.DUT14ZD208)
文摘A closed orientable Haken 3-manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation.Heegaard distance introduced by Hempel is a useful index in studying Heegaard splitting. This paper studies the stabilization problem for the bilateral self-amalgamation, and proves that if the distance of bilateral selfamalgamation of a Heegaard splitting is at least 9, then it is unstabilized, weakly reducible and irreducible.
基金supported by National Natural Science Foundation of China(Grant Nos.11329101 and 11101058)
文摘Let V ∪SW be a Heegaard splitting of M,such that αM = α-W = F1 ∪ F2 and g(S) = 2g(F1)= 2g(F2). Let V * ∪S*W * be the self-amalgamation of V ∪SW. We show if d(S) 3 then S* is not a topologically minimal surface.
