Abstract
The main subject of this talk is the following: The Topological Complexity of Algorithms Finding the Roots of Polynomials and Polynomial Systems.
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References
L. Blum, M. Shub, S. Smale, On a theory of computations over the real numbers; NP-completeness, recursive functions and universal machines, Bull. AMS 21: 1 (1989), 1–46.
D.B. Fuchs, Cohomology of braid groups mod 2, Funct. Anal. Appl. 4: 2(1970), 46–59.
Michael D. Hirsch, Applications of topology to lower bound estimates in computer science, preprint, International Computer Science Institute, 1990.
M.-H. Kim, Topological complexity of root-finding algorithms, J.Complexity 5: 3 (1989), 331–344.
H. Levine, A lower bound for the topological complexity of Poly(D, n), J. Complexity 5 (1989) 34–44.
A.S. Schwarz, The genus of a fibre bundle, Trans. Moscow Math. Soc. 10 (1961) 217–272.
G.B. Segal, Configuration-spaces and iterates loop-spaces, Invent. Math. 21: 3 (1973) 213–221.
S. Smale, On the topology of algorithms. I, J. Complexity 3: 2 (1987) 81–90.
V.A. Vasiliev, Cohomology of braid groups and complexity of algorithms, Funct. Anal. Appl. 22:3 (1988), 15–24.
———, Topological complexity of algorithms of approximate solving the systems of polynomial equations, Algebra Anal. 1:6 (1989) 198–213.
———, Topology of complements to discriminants and the loop-spaces, in Theory of Singularities and its Applications (V.I. Arnold, ed.), spaces, Advances in Soviet Mathematics, Vol. I, Publ. AMS, 1990, 9–21.
———, Topology of the spaces of functions without complicated singularities, Funct. Anal. Appl. 23:4 (1989), 24–36.
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© 1993 Springer-Verlag New York, Inc.
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Vassil’ev, V.A. (1993). Cohomology of Braid Groups and Complexity. In: Hirsch, M.W., Marsden, J.E., Shub, M. (eds) From Topology to Computation: Proceedings of the Smalefest. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2740-3_34
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DOI: https://doi.org/10.1007/978-1-4612-2740-3_34
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