Abstract
Let M be a simple manifold, and F be a component of ∂M of genus two. For a slope γ on F, we denote by M(γ) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of γ on F. In this paper, we shall prove that there is at most one separating slope γ on F such that M(γ) is ∂-reducible.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Scharlemann, M., Wu, Y.: Hyperbolic manifolds and degenerating handle additions. J. Austral. Math. Soc. Ser. A, 55, 72–89 (1993)
Zhang, M. X., Qiu, R. F., Li, Y. N.: The distance between two separating, reducing slopes is at most 4. Math. Z., 257, 799–810 (2007)
Scharlemann, M.: Refilling meridians in a genus 2 handlebody complement. Geometry & Topology Monographs, 14, 451–475 (2008)
Gordon, C., Luecke, J.: Reducible manifolds and Dehn surgery. Topology, 35, 385–409 (1996)
Wu, Y. Q.: The reducibility of surgered 3-manifolds. Topology Appl., 43, 213–218 (1992)
Culler, M., Gordon, C., Luecke, J., Shalen, P.: Dehn surgery on knots. Ann. Math., 125, 237–300 (1987)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by NSFC(10801021), NSFC(10625102), SRFDP(20050141011) and SRFDP(20070141035)
Rights and permissions
About this article
Cite this article
Li, Y.N., Qiu, R.F. & Zhang, M.X. Boundary reducible handle additions on simple 3-manifolds. Acta. Math. Sin.-English Ser. 25, 235–244 (2009). https://doi.org/10.1007/s10114-008-7119-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-008-7119-y