We introduce a “deformation” of plumbing. We also define a structure of data used in a calculation by computer aid of the crosscap numbers of alternating knots.

knot, spanning surface, plumbing, crosscap number, programming.

Received: June 5, 2021; Accepted: June 28, 2021; Published: August 13, 2021

How to cite this article: Noboru Ito and Kaito Yamada, Plumbing and computation of crosscap number, JP Journal of Geometry and Topology 26(2) (2021), 103-115. DOI: 10.17654/GT026020103

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] B. E. Clark, Crosscaps and knots, Internat. J. Math. Math. Sci. 1(1) (1978), 113-123.
[2] M. Hirasawa, Visualization of A’Campo’s fibered links and unknotting operation, Proceedings of the First Joint Japan-Mexico Meeting in Topology (Morelia, 1999) 121 (2002), 287-304.
[3] N. Ito and Y. Takimura, (1, 2) and weak (1, 3) homotopies on knot projections, J. Knot Theory Ramifications 22(14) (2013), 1350085, 14 pp.
[4] N. Ito and Y. Takimura, Crosscap number and knot projections, Internat. J. Math. 29(12) (2018), 1850084, 21 pp.
[5] N. Ito and Y. Takimura, Crosscap number of knots and volume bounds, Internat. J. Math. 31(13) (2020), 2050111, 33 pp.
[6] N. Ito and Y. Takimura, A lower bound of crosscap numbers of alternating knots, J. Knot Theory Ramifications 29(1) (2020), 1950092, 15 pp.
[7] M. Khovanov, Doodle groups, Trans. Amer. Math. Soc. 349(6) (1997), 2297-2315.
[8] T. Kindred, Crosscap numbers of alternating knots via unknotting splices, Internat. J. Math. 31(7) (2020), 2050057, 30 pp.
[9] M. Sakuma, Minimal genus Seifert surfaces for special arborescent links, Osaka J. Math. 31(4) (1994), 861-905.