Geodesic
Finitely Presented Groups and Semigroups in Knot Theory
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 231-248

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We construct finitely presented semigroups whose central elements are in one-to-one correspondence with the isotopy classes of non-oriented links in $\mathbb R^3$. Solving the word problem for those semigroups is equivalent to solving the classification problem for links and tangles. Also, we give a construction of finitely presented groups containing the braid group as a subgroup. 
@article{TM_2000_231_a7,
     author = {I. A. Dynnikov},
     title = {Finitely {Presented} {Groups} and {Semigroups} in {Knot} {Theory}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {231--248},
     publisher = {mathdoc},
     volume = {231},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2000_231_a7/}
}
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I. A. Dynnikov. Finitely Presented Groups and Semigroups in Knot Theory. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 231-248. http://geodesic.mathdoc.fr/item/TM_2000_231_a7/