An invariant of dichromatic links

An invariant of dichromatic links
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by Jim Hoste and Józef H. Przytycki PDF

Proc. Amer. Math. Soc. 105 (1989), 1003-1007 Request permission

We define a new polynomial invariant for a special class of dichromatic links. This polynomial generalizes the Jones polynomial.

References

P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett, and A. Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 2, 239–246. MR 776477, DOI 10.1090/S0273-0979-1985-15361-3
Jim Hoste and Mark E. Kidwell, Dichromatic link invariants, Trans. Amer. Math. Soc. 321 (1990), no. 1, 197–229. MR 961623, DOI 10.1090/S0002-9947-1990-0961623-2
V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987), no. 2, 335–388. MR 908150, DOI 10.2307/1971403
Louis H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), no. 3, 395–407. MR 899057, DOI 10.1016/0040-9383(87)90009-7
Kunio Murasugi, Jones polynomials of periodic links, Pacific J. Math. 131 (1988), no. 2, 319–329. MR 922222

Skein modules of

-manifolds

2

On Murasugi’s and Traczyk’s criteria for periodic links

Józef H. Przytycki and PawełTraczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1988), no. 2, 115–139. MR 945888
PawełTraczyk, $10_{101}$ has no period $7$: a criterion for periodic links, Proc. Amer. Math. Soc. 108 (1990), no. 3, 845–846. MR 1031676, DOI 10.1090/S0002-9939-1990-1031676-X