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1999 | 161 | 1-2 | 93-117
Tytuł artykułu

Spaces of polynomials with roots of bounded multiplicity

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.
Słowa kluczowe
Rocznik
Tom
161
Numer
1-2
Strony
93-117
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-12-14
poprawiono
1999-03-11
Twórcy
autor
autor
  • Department of Mathematics, Toyama International University, Kaminikawa, Toyama 930-1262, Japan, andrzej@tuins.ac.jp
autor
Bibliografia
  • [Ar] V. I. Arnold, Some topological invariants of algebraic functions, Trans. Moscow Math. Soc. 21 (1970), 30-52.
  • [Bo] C.-F. Bödigheimer, Stable splittings of mapping spaces, in: Algebraic Topology, H. R. Miller and D. C. Ravenel (eds.), Lecture Notes in Math. 1286, Springer, 1987, 174-187.
  • [CCMM] F. R. Cohen, R. L. Cohen, B. M. Mann and R. J. Milgram, The topology of rational functions and divisors of surfaces, Acta Math. 166 (1991), 163-221.
  • [CJS] R. L. Cohen, J. D. S. Jones and G. B. Segal, Floer's infinite dimensional Morse theory and homotopy theory, in: The Floer Memorial Volume, H. Hofer, C. H. Taubes, A. Weinstein and E. Zehnder (eds.), Progr. Math. 133, Birkhäuser, 1995, 297-325.
  • [Co] D. A. Cox, The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4 (1995), 17-50.
  • [Fu] K. Fukaya, Topological field theory and Morse theory, Sugaku Expositions 10 (1997), 19-39 (translation from Sūgaku 46 (1994), 289-307).
  • [GM] M. Goresky and R. MacPherson, Stratified Morse Theory, Springer, 1988.
  • [Gr] M. Gromov, Partial Differential Relations, Springer, 1986.
  • [Gu1] M. A. Guest, On the space of holomorphic maps from the Riemann sphere to the quadric cone, Quart. J. Math. 45 (1994), 57-75.
  • [Gu2] M. A. Guest, The topology of the space of rational curves on a toric variety, Acta Math. 174 (1995), 119-145.
  • [GKY1] M. A. Guest, A. Kozlowski and K. Yamaguchi, The topology of spaces of coprime polynomials, Math. Z. 217 (1994), 435-446.
  • [GKY2] M. A. Guest, A. Kozlowski and K. Yamaguchi, Stable splitting of the space of polynomials with roots of bounded multiplicity, J. Math. Kyoto Univ. 38 (1998), 351-366.
  • [Ha] A. Haefliger, Lectures on the theorem of Gromov, in: Proc. of Liverpool Singularities Symposium II, Lecture Notes in Math. 209, C. T. C. Wall (ed.), Springer, 1970, 128-141.
  • [JS] I. M. James and G. B. Segal, On equivariant homotopy type, Topology 17 (1978), 267-272.
  • [Kl1] S. Kallel, Particle spaces on manifolds and generalized Poincar\' e dualities, preprint.
  • [Kl2] S. Kallel, The topology of spaces of maps from a Riemann surface into complex projective space, preprint.
  • [Kt] F. Kato, Master's Thesis, Shinshu University, 1994 (in Japanese).
  • [KY] A. Kozlowski and K. Yamaguchi, Topology of complements of discriminants and resultants, preprint.
  • [Mc1] D. McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975), 91-107.
  • [Mc2] D. McDuff, Configuration spaces, in: K-Theory and Operator Algebras, Lecture Notes in Math. 575, Springer, 1977, 88-95.
  • [Po] V. Poenaru, Homotopy theory and differential singularities, in: Manifolds (Amsterdam, 1970), Lecture Notes in Math. 197, N. H. Kuiper (ed.), Springer, 1970, 106-133.
  • [Se1] G. B. Segal, Configuration spaces and iterated loop spaces, Invent. Math. 21 (1973), 213-221.
  • [Se2] G. B. Segal, The topology of spaces of rational functions, Acta Math. 143 (1979), 39-72.
  • [Se3] G. B. Segal, Some results in equivariant homotopy theory, unpublished manuscript.
  • [Va1] V. A. Vassiliev, Complements of Discriminants of Smooth Maps: Topology and Applications, Transl. Math. Monographs 98, Amer. Math. Soc., 1992 (rev. ed. 1994).
  • [Va2] V. A. Vassiliev, Topology of discriminants and their complements, in: Proc. Internat. Congress Math. 1994, Birkhäuser, 209-226.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv161i1p93bwm
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