The Heegaard Genus of Amalgamated 3-Manifolds
نویسندگان
چکیده
منابع مشابه
The Heegaard Genus of Amalgamated 3-manifolds
When studying Haken 3-manifolds, one is led naturally to the following construction: the amalgamation of two 3-manifolds M and M ′ via a homeomorphism between their boundaries. In this paper, we study the behaviour of Heegaard genus under this operation. We show that, provided the gluing homeomorphism is ‘sufficiently complicated’ and M and M ′ satisfy some standard conditions, then the Heegaar...
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Conversely, let F be a connected separating incompressible surface in a closed 3– manifold M′ and M1 and M2 the two manifolds obtained by cutting open M′ along F . Then one can construct a weakly reducible Heegaard splitting by amalgamating two splittings of M1 and M2 along F , see Scharlemann [13] for more detailed discussion. In [10] Lackenby showed that if M1 and M2 are simple and the gluing...
متن کاملHeegaard Stability in Amalgamated 3-manifolds I: Connected Sums
Let M1 and M2 be closed, irreducible 3-manifolds. Let Hi and Gi denote non-isotopic Heegaard surfaces in Mi, where Hi is unstabilized. Let H be the amalgamation of H1 and H2 and G be the amalgamation of G1 and G2 in M1#M2. Then H is not a stabilization of G. It follows that H and G are not isotopic, and that H is unstabilized. This answers a question of C. Gordon (Problem 3.91 from [Kir97]) in ...
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To this end let X and Y be 3–manifolds with incompressible boundary homeomorphic to a connected surface F . It is not difficult to show that if HX and HY are Heegaard surfaces in X and Y then we can amalgamate these splittings to obtain a Heegaard surface in X∪F Y with genus equal to g(HX)+g(HY )−g(F) (see, for example, Schultens [14]). Letting g(X), g(Y), and g(X∪F Y) denote the minimal genus ...
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Acknowledgements My foremost thanks are to my supervisor Roman Nedela, for his continual encouragement, support and patience, for many inspirational conversations, leading me in the times of hasitations and careful reading many versions of the draft. Thanks also to Peter Maličk´y for the effort with some computations with groups and many advices in topology. Thanks also to Mathematical Institut...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2004
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-004-6553-y