Knots in S 2 x S 1 derived from Sym(2, ℝ)

Sang Lee; Yongdo Lim; Chan-Young Park

Fundamenta Mathematicae (2000)

  • Volume: 164, Issue: 3, page 241-252
  • ISSN: 0016-2736

Abstract

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We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in S 2 × S 1 and show that these knots or links have certain types of symmetry of period 2.

How to cite

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Lee, Sang, Lim, Yongdo, and Park, Chan-Young. "Knots in $S^2 x S^1$ derived from Sym(2, ℝ)." Fundamenta Mathematicae 164.3 (2000): 241-252. <http://eudml.org/doc/212455>.

@article{Lee2000,
abstract = {We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in $S^2 × S^1$ and show that these knots or links have certain types of symmetry of period 2.},
author = {Lee, Sang, Lim, Yongdo, Park, Chan-Young},
journal = {Fundamenta Mathematicae},
keywords = {geodesic; symmetric matrix; Shilov boundary; 2-periodic knot; geodesics},
language = {eng},
number = {3},
pages = {241-252},
title = {Knots in $S^2 x S^1$ derived from Sym(2, ℝ)},
url = {http://eudml.org/doc/212455},
volume = {164},
year = {2000},
}

TY - JOUR
AU - Lee, Sang
AU - Lim, Yongdo
AU - Park, Chan-Young
TI - Knots in $S^2 x S^1$ derived from Sym(2, ℝ)
JO - Fundamenta Mathematicae
PY - 2000
VL - 164
IS - 3
SP - 241
EP - 252
AB - We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in $S^2 × S^1$ and show that these knots or links have certain types of symmetry of period 2.
LA - eng
KW - geodesic; symmetric matrix; Shilov boundary; 2-periodic knot; geodesics
UR - http://eudml.org/doc/212455
ER -

References

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  1. [1] W. Bertram, Un théorème de Liouville pour les algèbres de Jordan, Bull. Soc. Math. France 124 (1996), 299-327. 
  2. [2] J. Faraut and A. Korányi, Analysis on Symmetric Cones, Oxford Univ. Press, Oxford, 1994. Zbl0841.43002
  3. [3] R. H. Fox, Knots and periodic transformations, in: Topology of 3-Manifolds and Related Topics (Proc. Univ. of Georgia Institute, 1961), Prentice-Hall, 1962, 177-182. 
  4. [4] K. W. Kwun, Piecewise linear involutions of S 1 × S 2 , Michigan Math. J. 16 (1969), 93-96. 
  5. [5] S. Y. Lee, Y. Lim and C.-Y. Park, Symmetric geodesics on conformal compactifications of Euclidean Jordan algebras, Bull. Austral. Math. Soc. 59 (1999), 187-201. Zbl0977.53038
  6. [6] B. Makarevich, Ideal points of semisimple Jordan algebras, Mat. Zametki 15 (1974), 295-305 (in Russian). 
  7. [7] J. W. Morgan and H. Bass, The Smith Conjecture, Academic Press, 1984. Zbl0599.57001
  8. [8] D. Rolfsen, Knots and Links, Publish or Perish, 1976. 
  9. [9] P. A. Smith, Transformations of finite period II, Ann. of Math. 40 (1939), 690-711. Zbl0021.43002
  10. [10] Y. Tao, On fixed point free involutions of S 1 × S 2 , Osaka Math. J. 14 (1962), 145-152. 
  11. [11] J. L. Tollefson, Involutions on S 1 × S 2 and other 3-manifolds Trans. Amer. Math. Soc. 183 (1973), 139-152. Zbl0276.57001

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