Celebratio Mathematica — Scharlemann

Complete Bibliography

Works connected to Ying-Qing Wu

Filter the Bibliography List

year	title	people

			clear

M. Scharlemann and Y. Q. Wu: “Hyperbolic manifolds and degenerating handle additions,” J. Austral. Math. Soc. Ser. A 55 : 1 (August 1993), pp. 72–89. MR 1231695 Zbl 0802.57005 article

A 2-handle addition on the boundary of a hyperbolic 3-manifold \( M \) is called degenerating if the resulting manifold is not hyperbolic. There are examples that some manifolds admit infinitely many degenerating handle additions. But most of them are not ‘basic’. (See Section 1 for definitions). Our first main theorem shows that there are only finitely many basic degenerating handle additions. We also study the case that one of the handle additions produces a reducible manifold, and another produces a \( \partial \)-reducible manifold, showing that in this case either the two attaching curves are disjoint, or they can be isotoped into a once-punctured torus. A byproduct is a combinatorial proof of a similar known result about degenerating hyperbolic structures by Dehn filling.