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A Note on Heegaard Splittings of Amalgamated 3-Manifolds |
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| Authors: | Kun DU and Xutao GAO |
| Affiliation: | 1. School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,China 2. School of Mathematical Science,Dalian University of Technology,Dalian 116024,Liaoning,China |
| Abstract: | 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(M1) + g(M2) -g(F)) + 1, then g(M) = g(M1) + g(M2) - g(F). |
| Keywords: | Distance Stabilization Strongly irreducible |
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