An exact sequence for generalized string links over surfaces
Keywords:braid groups, homotopy groups, generalized string links, presentation of braids, string link groups
In this work we extend Goldberg result  for generalized string links over closed, connected and orientable surfaces of genus $g \geq 1$, i.e., different from the sphere (up to link-homotopy).
Artin, E. Theory of braids. Annals of Mathematics (1947), 101–126.
Birman, J. S. Braids, Links, and Mapping Class Groups., vol. 82. Princeton University Press, 2016.
Dehornoy, P., Dynnikov, I., Rolfsen, D., and Wiest, B. Ordering braids. No. 148. American Mathematical Soc., 2008.
Goldberg, C. H. An exact sequence of braid groups. Mathematica Scandinavica 33, 1 (1974), 69–82.
Goldsmith, D. L. Homotopy of braids: in answer to a question of E. Artin. In Topology Conference (1974), Springer, pp. 91–96.
Gonzalez-Meneses, J. New presentations of surface braid groups. Journal of Knot Theory and Its Ramifications 10, 03 (2001), 431–451.
Gonzalez-Meneses, J. Ordering pure braid groups on compact, connected surfaces. Pacific Journal of Mathematics 203, 2 (2002), 369–378.
Habegger, N., and Lin, X.-S. The classification of links up to link-homotopy. Journal of the American Mathematical Society 3, 2 (1990), 389–419.
Levine, J. P. An approach to homotopy classification of links. Transactions of the American Mathematical Society 306, 1 (1988), 361–387.
Lingua, F., Wang, W., Shpani, L., and Capogrosso-Sansone, B. A topological signature of multipartite entanglement. arXiv preprint arXiv:1905.07454 (2019).
Milnor, J. Link groups. Annals of Mathematics (1954), 177–195.
Theodoro de Lima, J. R. Homotopy of braids on surfaces: Extending goldsmith’s answer to artin. Journal of Knot Theory and Its Ramifications 28, 12 (2019), 1950072.
Theodoro de Lima, J. R., and de Mattos, D. Ordering homotopy string links over surfaces. Journal of Knot Theory and Its Ramifications 25, 01 (2016), 1650001.
Yurasovskaya, E. Homotopy string links over surfaces. PhD thesis, University of British Columbia, 2008.
How to Cite
Copyright (c) 2023 Juliana Roberta Theodoro de Lima
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors may enter into separate non-commercial contractual agreements for the non-exclusive distribution of the journal's published version of the work (for example, posting it in an institutional repository or publishing it in a book), with an acknowledgment of its initial publication in this journal.