RESEARCH ARTICLE

Essential closed surfaces in surface sum of product I-bundle of closed surfaces

  • Shuxin WANG
Expand
  • School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received date: 17 Dec 2010

Accepted date: 14 Jul 2011

Published date: 01 Oct 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

In this paper, we will give some results on the classification of essential closed surfaces in the surface sum of product I-bundle of closed surfaces and some applications of these results.

Cite this article

Shuxin WANG . Essential closed surfaces in surface sum of product I-bundle of closed surfaces[J]. Frontiers of Mathematics in China, 2011 , 6(5) : 945 -956 . DOI: 10.1007/s11464-011-0150-9

1
Du Kun, Ma Jiming, Qiu Ruifeng, Zhang Mingxing. Heegaard genera of annular 3-manifolds. Journal of Knot and Its Ramifications, 2011, 20(4): 547-566

DOI

2
Hempel J. 3-Manifolds. Princeton: Princeton University Press, 1976

3
Herbert C. Incompressible surfaces in knot spaces. T Am Math Soc, 1971, 157: 53-62

DOI

4
Jaco W. Lectures on Three-manifold Topology. CBMS, Regional Conference Series in Mathematics, No 43. Providence: Am Math Soc, 1980

5
Li Fengling, Yang Guoqiu, Lei Fengchun. Heegaard genera of high distance are additive under annulus sum. Topology and Its Application, 2010, 157: 1188-1194

DOI

6
Qiu Ruifeng, Wang Shicheng, Zhang Mingxing. Additivity of Heegaard genera of bounded surface sums. Topology and Its Application, 2010, 157: 1593-1601

DOI

7
Scharlemmann M. Proximity in the curve complex: boundary reduction and bicompressible surfaces. Pacific J Math, 2006, 228: 325-348

DOI

Options
Outlines

/