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CYCLIC PRESENTATIONS AND TORUS KNOTS K(d, 2)

Yıl 2011, Cilt: 4 Sayı: 2, 125 - 133, 12.03.2014

Öz

In this paper, we have shown that the polynomials associated with the cyclically presented groups obtained from the word w generated with Dunwoody parameters 1 1 1 3 2 2 2 2 (1, ,0, 2),(1, k k,0, k),( k ,1,0, k ),( k ,1,0, k ) , where k is an odd positive integer and d  k  2 , coincide (up to sign)
with the Alexander polynomial of the torus knot K(d,2) .

Kaynakça

  • Ankaralioglu, N., Aydin, H. 2008. Some Dunwoody parameters and cyclic presentations. General Mathematics, 16(2), 85–93.
  • Aydin, H., Gultekin, I. and Mulazzani, M. 2003. Torus Knots and Dunwoody Manifolds. Siberian Math. J., 45, 1-6.
  • Burde, G., Zieschang, H. 1985. Knots, Berlin, New York, Walter de Gruyter.
  • Cattabriga, A., Mulazzani, M. 2005. Representations of (1,1)-knots, Fundamenta Mathematicae., 188, 45-57.
  • Cavicchioli, A., Hegenbarth, F., Kim, A.C. 1999. On Cyclic Branched Covering of Torus Knots. J. Geom., 64, 55-66.
  • Cavicchioli, A., Ruini, B., Spaggiari,F. 2001. On a Conjecture of M. J. Dunwoody. Algebra colloq., 8, 169-218.
  • Dunwoody, M. J. Cyclic Presentations and 3-Manifolds. In Proc. Inter Conf., Groups Korea’94, Walter De Gruyter, 47-55, 1995, Berlin, New York.
  • Graselli, L., Mulazzani, M. 2001. Genus one 1-bridge knots and Dunwoody manifolds. Forum Math. 13, 379–397.
  • Johnson, D.L., (1990). Presentations of Groups. Cambridge University Press. ****
Yıl 2011, Cilt: 4 Sayı: 2, 125 - 133, 12.03.2014

Öz

Kaynakça

  • Ankaralioglu, N., Aydin, H. 2008. Some Dunwoody parameters and cyclic presentations. General Mathematics, 16(2), 85–93.
  • Aydin, H., Gultekin, I. and Mulazzani, M. 2003. Torus Knots and Dunwoody Manifolds. Siberian Math. J., 45, 1-6.
  • Burde, G., Zieschang, H. 1985. Knots, Berlin, New York, Walter de Gruyter.
  • Cattabriga, A., Mulazzani, M. 2005. Representations of (1,1)-knots, Fundamenta Mathematicae., 188, 45-57.
  • Cavicchioli, A., Hegenbarth, F., Kim, A.C. 1999. On Cyclic Branched Covering of Torus Knots. J. Geom., 64, 55-66.
  • Cavicchioli, A., Ruini, B., Spaggiari,F. 2001. On a Conjecture of M. J. Dunwoody. Algebra colloq., 8, 169-218.
  • Dunwoody, M. J. Cyclic Presentations and 3-Manifolds. In Proc. Inter Conf., Groups Korea’94, Walter De Gruyter, 47-55, 1995, Berlin, New York.
  • Graselli, L., Mulazzani, M. 2001. Genus one 1-bridge knots and Dunwoody manifolds. Forum Math. 13, 379–397.
  • Johnson, D.L., (1990). Presentations of Groups. Cambridge University Press. ****
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Nurullah Ankaralıoğlu

Hüseyin Aydın

Yayımlanma Tarihi 12 Mart 2014
Yayımlandığı Sayı Yıl 2011 Cilt: 4 Sayı: 2

Kaynak Göster

APA Ankaralıoğlu, N., & Aydın, H. (2014). CYCLIC PRESENTATIONS AND TORUS KNOTS K(d, 2). Erzincan University Journal of Science and Technology, 4(2), 125-133.