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Tytuł artykułu

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

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Abstrakty

EN
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.

Słowa kluczowe

Twórcy

  • Department of Mathematics, College of Natural Sciences, Pusan National University, Pusan 609-735, Republic of Korea
autor
  • Department of Mathematics, College of Natural Sciences, Pusan National University, Pusan 609-735, Republic of Korea
  • Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Republic of Korea

Bibliografia

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  • [2] J. Faraut and A. Korányi, Analysis on Symmetric Cones, Oxford Univ. Press, Oxford, 1994.
  • [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] K. W. Kwun, Piecewise linear involutions of $S^1 × S^2$, Michigan Math. J. 16 (1969), 93-96.
  • [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.
  • [6] B. Makarevich, Ideal points of semisimple Jordan algebras, Mat. Zametki 15 (1974), 295-305 (in Russian).
  • [7] J. W. Morgan and H. Bass, The Smith Conjecture, Academic Press, 1984.
  • [8] D. Rolfsen, Knots and Links, Publish or Perish, 1976.
  • [9] P. A. Smith, Transformations of finite period II, Ann. of Math. 40 (1939), 690-711.
  • [10] Y. Tao, On fixed point free involutions of $S^1 × S^2$, Osaka Math. J. 14 (1962), 145-152.
  • [11] J. L. Tollefson, Involutions on $S^1 × S^2$ and other 3-manifolds Trans. Amer. Math. Soc. 183 (1973), 139-152.

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