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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- [8] W. Magnus, A. Karras and D. Solitar, Combinatorial Group Theory, Wiley Interscience, New York, 1966.
- [9] S. Plotnik, Equivariant intersection forms, knots in , 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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