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Volume 29, Issue 2
A Kind of Essential Surfaces in the Complements of Knots

Youfa Han, shengjun Pan & Shuxin Wang

Commun. Math. Res., 29 (2013), pp. 143-147.

Published online: 2021-05

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  • Abstract

In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which improves the estimation of the Euler characteristic of the essential surfaces with boundaries under certain conditions. Furthermore, we give the genus of the essential surfaces.

  • Keywords

essential surface, twist-crossing number, almost alternating knot, reduced graph.

  • AMS Subject Headings

57M15, 57M25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-29-143, author = {Han , YoufaPan , shengjun and Wang , Shuxin}, title = {A Kind of Essential Surfaces in the Complements of Knots}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {2}, pages = {143--147}, abstract = {

In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which improves the estimation of the Euler characteristic of the essential surfaces with boundaries under certain conditions. Furthermore, we give the genus of the essential surfaces.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19017.html} }
TY - JOUR T1 - A Kind of Essential Surfaces in the Complements of Knots AU - Han , Youfa AU - Pan , shengjun AU - Wang , Shuxin JO - Communications in Mathematical Research VL - 2 SP - 143 EP - 147 PY - 2021 DA - 2021/05 SN - 29 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19017.html KW - essential surface, twist-crossing number, almost alternating knot, reduced graph. AB -

In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which improves the estimation of the Euler characteristic of the essential surfaces with boundaries under certain conditions. Furthermore, we give the genus of the essential surfaces.

Han , YoufaPan , shengjun and Wang , Shuxin. (2021). A Kind of Essential Surfaces in the Complements of Knots. Communications in Mathematical Research . 29 (2). 143-147. doi:
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