Sweepouts of amalgamated 3–manifolds
نویسندگان
چکیده
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 among all Heegaard surfaces in the respective 3–manifolds, we find:
منابع مشابه
2 00 5 Sweepouts of Amalgamated 3 - Manifolds
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