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- Title
A note on Heegaard splittings of amalgamated 3-manifolds.
- Authors
Du, Kun; Gao, Xutao
- 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 M and M. If M has a minimal Heegaard splitting M = % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbaGaemOvay1aaSbaaSqaaiabdMgaPbqabaqeduuDJXwA % KbYu51MyVXgaiyaakiab-PIiipaaBaaaleaacqWGibasdaWgaaadba % GaemyAaKgabeaaaSqabaaaaa!4710! $$ V_i \cup _{H_i } $$ W with d( H) + d( H) ≥ 2( g( M) + g( M) − g( F)) + 1, then g( M) = g( M 1) + g( M 2) − g( F).
- Subjects
TOPOLOGY; MANIFOLDS (Mathematics); HANDLEBODIES; MATHEMATICAL proofs; MATHEMATICAL analysis; DISTANCES; CURVES
- Publication
Chinese Annals of Mathematics, 2011, Vol 32, Issue 3, p475
- ISSN
0252-9599
- Publication type
Article
- DOI
10.1007/s11401-011-0641-8