# High-dimensional knots corresponding to the fractional Fibonacci groups

Andrzej Szczepański; Andreĭ Vesnin

Fundamenta Mathematicae (1999)

- Volume: 161, Issue: 1-2, page 235-240
- ISSN: 0016-2736

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topSzczepański, Andrzej, and Vesnin, Andreĭ. "High-dimensional knots corresponding to the fractional Fibonacci groups." Fundamenta Mathematicae 161.1-2 (1999): 235-240. <http://eudml.org/doc/212403>.

@article{Szczepański1999,

abstract = {We prove that the natural HNN-extensions of the fractional Fibonacci groups are the fundamental groups of high-dimensional knot complements. We also give some characterization and interpretation of these knots. In particular we show that some of them are 2-knots.},

author = {Szczepański, Andrzej, Vesnin, Andreĭ},

journal = {Fundamenta Mathematicae},

keywords = {fiber 2-knot; HNN-extension},

language = {eng},

number = {1-2},

pages = {235-240},

title = {High-dimensional knots corresponding to the fractional Fibonacci groups},

url = {http://eudml.org/doc/212403},

volume = {161},

year = {1999},

}

TY - JOUR

AU - Szczepański, Andrzej

AU - Vesnin, Andreĭ

TI - High-dimensional knots corresponding to the fractional Fibonacci groups

JO - Fundamenta Mathematicae

PY - 1999

VL - 161

IS - 1-2

SP - 235

EP - 240

AB - We prove that the natural HNN-extensions of the fractional Fibonacci groups are the fundamental groups of high-dimensional knot complements. We also give some characterization and interpretation of these knots. In particular we show that some of them are 2-knots.

LA - eng

KW - fiber 2-knot; HNN-extension

UR - http://eudml.org/doc/212403

ER -

## References

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- [6] A. Kim and A. Vesnin, A topological study of the fractional Fibonacci groups, Siberian Math. J. 39 (1998).
- [7] C. MacLachlan, Generalizations of Fibonacci numbers, groups and manifolds, in: Combinatorial and Geometric Group Theory (Edinburgh, 1993), A. J. Duncan, N. D. Gilbert and J. Howie (eds.), London Math. Soc. Lecture Note Ser. 204, Cambridge Univ. Press, 1995, 233-238. Zbl0851.20026
- [8] W. Magnus, A. Karras and D. Solitar, Combinatorial Group Theory, Wiley Interscience, New York, 1966.
- [9] S. Plotnik, Equivariant intersection forms, knots in ${S}^{4}$, and rotations in 2-spheres, Trans. Amer. Math. Soc. 296 (1986), 543-575.
- [10] D. Rolfsen, Knots and Links, Publish or Perish, Berkeley, CA, 1976.
- [11] A. Szczepański, High dimensional knot groups and HNN extensions of the Fibonacci groups, J. Knot Theory Ramifications 7 (1998), 503-508. Zbl0908.57005
- [12] C. Zeeman, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965), 471-495. Zbl0134.42902

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