On the Alexander polynomial of a cyclically periodic knot
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- by Jonathan A. Hillman PDF
- Proc. Amer. Math. Soc. 89 (1983), 155-156 Request permission
Abstract:
We show that a theorem of Burde on the Alexander polynomial of a cyclically periodic knot $K$, such that ${\Delta _2}(K) = 1$, may be extended to all cyclically periodic knots.References
- Gerhard Burde, Über periodische Knoten, Arch. Math. (Basel) 30 (1978), no. 5, 487–492 (German). MR 645216, DOI 10.1007/BF01226090
- C. McA. Gordon, R. A. Litherland, and K. Murasugi, Signatures of covering links, Canadian J. Math. 33 (1981), no. 2, 381–394. MR 617628, DOI 10.4153/CJM-1981-032-3
- Jonathan A. Hillman, New proofs of two theorems on periodic knots, Arch. Math. (Basel) 37 (1981), no. 5, 457–461. MR 643289, DOI 10.1007/BF01234382
- Ulrich Lüdicke, Zyklische Knoten, Arch. Math. (Basel) 32 (1979), no. 6, 588–599 (German). MR 550326, DOI 10.1007/BF01238545
- Kunio Murasugi, On periodic knots, Comment. Math. Helv. 46 (1971), 162–174. MR 292060, DOI 10.1007/BF02566836
- Kunio Murasugi, On symmetry of knots, Tsukuba J. Math. 4 (1980), no. 2, 331–347. MR 623446, DOI 10.21099/tkbjm/1496159185
- Makoto Sakuma, On the polynomials of periodic links, Math. Ann. 257 (1981), no. 4, 487–494. MR 639581, DOI 10.1007/BF01465869
- H. F. Trotter, Periodic automorphisms of groups and knots, Duke Math. J. 28 (1961), 553–557. MR 133820
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 155-156
- MSC: Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-1983-0706531-9
- MathSciNet review: 706531