Braid Group Cohomologies and Algorithm Complexity
نویسنده
چکیده
Smale's method is of very general character: it provides an estimate of the topological complexity of any nonlinear ill-posed problem by means of a topological characteristic of the corresponding fibration, namely, its genus introduced and studied by Shvarts in[7] (and rediscovered in [8]). In the case of the problem on polynomial roots, an estimate of the genus [of which the inequality (i) is a corollary] was proved in [8] by means of Fuks' results on Artin's braid group cohomologies [4]. The right-hand part estimate in (2) is based on a more detailed study of these cohomologies.
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Cohomology of Artin groups of type Ãn , Bn and applications
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