Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A generalization of the handle addition theorem


Author: Ying Qing Wu
Journal: Proc. Amer. Math. Soc. 114 (1992), 237-242
MSC: Primary 57N10; Secondary 57M25, 57M99
DOI: https://doi.org/10.1090/S0002-9939-1992-1070535-5
MathSciNet review: 1070535
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We will generalize Jaco's Handle Addition Theorem to the $ n$-compressibility of surfaces on the boundary of $ 3$-manifolds. Several corollaries are given that show how the theorem can be applied to different situations.


References [Enhancements On Off] (What's this?)

  • [1] A. Casson and C. Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987), 275-283. MR 918537 (89c:57020)
  • [2] M. Culler, C. Gordon, J. Luecke, and P. Shalen, Dehn surgery on knots, Ann. of Math. (2) 125 (1987), 237-300. MR 881270 (88a:57026)
  • [3] C. Gordon, On primitive sets of loops in the boundary of a handlebody, Topology Appl. 27 (1987), 285-299. MR 918538 (88k:57013)
  • [4] W. Jaco, Adding a $ 2$-handle to $ 3$-manifold: an application to property $ R$, Proc. Amer. Math. Soc. 92 (1984), 288-292. MR 754723 (86b:57006)
  • [5] K. Johannson, On surfaces in one-relator $ 3$-manifolds, Low-Dimensional Topology and Kleinian Groups, London Math. Soc. Lecture Notes Sci. 112 (1984), 157-192. MR 903864 (89m:57014)
  • [6] J. H. Przytycki, Incompressibility of surfaces after Dehn surgery, Michigan Math. J. 30 (1983), 289-308. MR 725782 (86g:57012)
  • [7] M. Scharlemann, Outermost forks and a theorem of Jaco, Proc. Rochester Conf., 1982.
  • [8] Y-Q. Wu, Incompressibility of surfaces in surgered $ 3$-manifolds, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N10, 57M25, 57M99

Retrieve articles in all journals with MSC: 57N10, 57M25, 57M99


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1070535-5
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society