Abstract:
Complements to discriminants of singularities of smooth functions are far generalizations of the classifying spaces of Artin and Brieskorn braid groups. A group of stable cohomologies (i.e., cohomologies preserved under adjacency of singularities) is described for these spaces. A relationship between these cohomologies and Gauss–Manin connectivity of singularities is indicated. A cellular realization of cohomologies of symmetric groups with coefficients in Z2Z2 is described.
Citation:
V. A. Vassiliev, “Stable cohomology of complements to the discriminants of deformations of singularities of smooth functions”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 33, VINITI, Moscow, 1988, 3–29; J. Soviet Math., 52:4 (1990), 3217–3230
\Bibitem{Vas88}
\by V.~A.~Vassiliev
\paper Stable cohomology of complements to the discriminants of deformations of singularities of smooth functions
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1988
\vol 33
\pages 3--29
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd105}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=967763}
\zmath{https://zbmath.org/?q=an:0731.55012|0900.55005}
\transl
\jour J. Soviet Math.
\yr 1990
\vol 52
\issue 4
\pages 3217--3230
\crossref{https://doi.org/10.1007/BF01095248}
Linking options:
https://www.mathnet.ru/eng/intd105
https://www.mathnet.ru/eng/intd/v33/p3
This publication is cited in the following 8 articles:
Victor A. Vassiliev, “Complements of discriminants of simple real function singularities”, Isr. J. Math., 2024
V. A. Vassiliev, “Homology groups of spaces of non-resultant quadratic polynomial systems in R3”, Izv. Math., 80:4 (2016), 791–810
Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin, Global Aspects of Complex Geometry, 2006, 171
Thomas Keilen, “Smoothness of equisingular families of curves”, Trans. Amer. Math. Soc., 357:6 (2004), 2467
V. A. Vassiliev, “Spaces of Hermitian operators with simple spectra and their finite-order cohomology”, Mosc. Math. J., 3:3 (2003), 1145–1165
V. A. Vassiliev, “How to Calculate Homology Groups of Spaces of Nonsingular Algebraic Projective Hypersurfaces”, Proc. Steklov Inst. Math., 225 (1999), 121–140
V. A. Vassiliev, “On the topology of spaces of functions without complex singularities”, Russian Math. Surveys, 44:3 (1989), 218–219
V. A. Vassiliev, “Topology of spaces of functions without compound singularities”, Funct. Anal. Appl., 23:4 (1989), 277–286
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