Celebratio Mathematica — Rourke — Complete Bibliography

Complete Bibliography

Works connected to Richard Rimányi

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R. Fenn, R. Rimányi, and C. Rourke: “Some remarks on the braid-permutation group,” pp. 57–68 in Topics in knot theory. NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 399. Kluwer (Dordrecht), 1993. MR 1257905 Zbl 0830.57005 incollection

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Richard Rimányi	Related

R. Fenn, R. Rimányi, and C. Rourke: “The braid-permutation group,” Topology 36 : 1 (1997), pp. 123–135. MR 1410467 Zbl 0861.57010 article

We consider the subgroup of the automorphism group of the free group generated by the braid group and the permutation group. This is proved to be the same as the subgroup of automorphisms of permutation-conjugacy type and is represented by generalised braids (braids in which some crossings are allowed to be “welded”). As a consequence of this representation there is a finite presentation which shows the close connection with both the classical braid and permutation groups. The group is isomorphic to the automorphism group of the free quandle and closely related to the automorphism group of the free rack. These automorphism groups are connected with invariants of classical knots and links in the 3-sphere.

Roger Fenn	Related
Richard Rimányi	Related