Abstract
There exists an analogy between algebraic functions and vector fiberings, the role of Grassmann’s manifold being played by the space K(π, 1) of an alternating group. Among the cohomology classes of a complement of the branching manifold of an algebraic function there exist classes induced by the cohomology classes of an alternating group. Some of these classes (in any case the modulo-2 one-dimensional class and the three-dimensional class) are invariant under a Tschirnhausen transformation. Hence follows, for example, that the function w(a, b, c), defined by the equation w4 + aw2 + bw + c = 0, cannot be represented by a Tschirnhausen transformation with polynomial coefficients of any algebraic function z(u, v) of two variables u and v that are polynomials of a, b, and c.
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© 1970 Ukrain. Acad. Sciences, Kiev
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Arnold, V.I. (1970). Trivial problems. In: Givental, A., Khesin, B., Varchenko, A., Vassiliev, V., Viro, O. (eds) Vladimir I. Arnold - Collected Works. Vladimir I. Arnold - Collected Works, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31031-7_20
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DOI: https://doi.org/10.1007/978-3-642-31031-7_20
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