# Upper singular braid monoid SBn+

## Keywords:

Braid, Upper singular braid, Upper singular braid monoids## Abstract

The purpose of this paper is to describe the structure of SB n+monoids and prove some new properties. The second purpose of the article is to present the experience carried out with mathematics teachers and students from 17 to 21 years old concerning SB n + monoids and observe how these concepts were perceived.

## References

E. Artin, (1925). Theorie der Zöpfe, Abhandlungen aus dem Mathematischen, Abh. Math. Sem. Univ. Hamburg 4, pp. 47-72.

E. Artin, (1947). Theory of braids, Annals of Math. (2) 48, pp. 101-126.

J.C. Baez, (1992). Link invariants of finite type and perturbation theory, Lett. Math. Phys. 26, no.1, pp. 43-51.

J.S. Birman, (1974). Braids, Links and Mapping Class Groups, Annals of Math. Studies 82, Princeton Univ. Press.

J.S. Birman, (1993). New points of view in knot theory, Bull. Amer. Math. Soc. (N.S.) 28, no.2, pp. 253-287.

J.S. Birman, K.H. Ko, S.J. Lee, (1998). A new approach to the word and the conjugacy problem in the braid groups, Adv. Math. 139, pp. 322-353.

O. Bogopolski, (2008). Introduction to Group Theory, European Mathematical Society Publishing House, Zürich.

B.A. Cisneros De la Cruz, G. Gandolfi, (2019). Algebraic, combinatorial and topological properties of singular virtual braid monoids, Journal of Knot Theory and Its Ramifications, Vol. 28 (10), 1950069.

R. Fenn, R. Rimanyi, C. Rourke, (1997). The braid-permutation group, Topology vol. 36, No. 1, pp. 123-135.

F.A. Garside, (1969). The braid group and other groups, Quart. J. Math. Oxford Ser. 20, pp. 235–254.

D.L. Johnson, (1997). Presentations of groups, Cambridge University Press, United Kingdom.

V. Jugé, (2016). Combinatorics of braids, PhD Thesis.http://www-igm.univ-mlv.fr/~juge/papers/PhD-Thesis.pdf

E.-K. Lee, (2010). A positive presentation for the pure braid group, Journal of the Chungcheong Mathematical Society, Vol. 23, No. 3, pp. 555-561.

P. Ligouras, (2020). Semigroups, monoids and free groups, Experiences of Teaching with Mathematics, Sciences and Technology, ISSN 2421-7247, Vol. 5, pp. 515-526.

V. Lin, (2004). Braids and Permutations, Arxiv: math.GR/0404528.

R.C. Lyndon, P.E. Schupp, (1977). Combinatorial group theory, Springer-Verlag, Berlin, Heidelberg, New York.

W. Magnus, A. Karrass, D. Solitar, (1976). Combinatorial group theory, Dover Publ. Inc., NewYork.

S. Moran, (1983). The Mathematical Theory of Knots and Braids, North–Holland Mathematics Studies, vol. 82, Elsevier, Amsterdam.

L. Paris, (2009). Braid groups and Artin groups, in A. Papadopoulos (editor), Handbook of Teichmüller Theory, Volume II, European Mathematical Society Publishing House, Zürich.

D.J.S. Robinson, (2003). An introduction to abstract algebra, Walter de Gruyter, Berlin.

J.J. Rotman, (1995). An introduction to the theory of groups, 4 th ed., Springer-Verlag New York, Ine.

V. Vershinin, (2010). On the singular braid monoid, St. Petersburg Math. J., Vol. 21, No. 5, pp.693-704.

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*EDiMaST: Experiences of Teaching With Mathematics, Sciences and Technology*,

*5*, 675–687. Retrieved from https://www.edimast.it/index.php/edimast/article/view/68

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Copyright (c) 2019 Panagiote Ligouras

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