Essential closed surfaces in surface sum of product <italic>I</italic>-bundle of closed surfaces

Shuxin WANG

doi:10.1007/s11464-011-0150-9

PDF(143 KB)

Front. Math. China ›› 2011, Vol. 6 ›› Issue (5) : 945-956. DOI: 10.1007/s11464-011-0150-9

RESEARCH ARTICLE

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

Shuxin WANG

Author information +

History +

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.

Keywords

Surface sum / product I-bundle / essential surface / Haken-Kneser number

Cite this article

EndNote

Ris (Procite)

Bibtex

Download citation ▾

Shuxin WANG. Essential closed surfaces in surface sum of product I-bundle of closed surfaces. Front Math Chin, 2011, 6(5): 945‒956 https://doi.org/10.1007/s11464-011-0150-9

References

Publishing order | Descend order by publishing year | Descend order by cited within

[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 CrossRef Google scholar

[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 CrossRef Google scholar

[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 CrossRef Google scholar

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

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