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- W2284206962 abstract "We introduce a new technique for finding lower bounds on the Heegaard genus of a 3-manifold obtained by gluing a pair of 3-manifolds together along an incompressible torus or annulus. We deduce a number of inequalities, including one which implies that $t(K_1# K_2)geq max {t(K_1),t(K_2)}$, where $t(-)$ denotes tunnel number, $K_1$ and $K_2$ are knots in $S^3$, and $K_1$ is $m$-small. This inequality is best possible. We also provide an interesting collection of examples, similar to a set of examples found by Schultens and Wiedmann, which show that Heegaard genus can stay persistently low under the kinds of gluings we study here." @default.
- W2284206962 created "2016-06-24" @default.
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- W2284206962 date "2012-11-19" @default.
- W2284206962 modified "2023-09-27" @default.
- W2284206962 title "On Heegaard splittings of glued 3-manifolds" @default.
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