Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya"
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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 1988, Volume 33, Pages 3–29 (Mi intd105)  

This article is cited in 5 scientific papers (total in 5 papers)

Stable cohomology of complements to the discriminants of deformations of singularities of smooth functions

V. A. Vassiliev


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 $Z_2$ is described.

Full text: PDF file (1656 kB)

English version:
Journal of Soviet Mathematics, 1990, 52:4, 3217–3230

Bibliographic databases:

UDC: 515.164.15+515.172.23

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

Citation in format AMSBIB
\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://www.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}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Vassiliev, “On the topology of spaces of functions without complex singularities”, Russian Math. Surveys, 44:3 (1989), 218–219  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Vassiliev, “Topology of spaces of functions without compound singularities”, Funct. Anal. Appl., 23:4 (1989), 277–286  mathnet  crossref  mathscinet  zmath  isi
    3. V. A. Vassiliev, “How to Calculate Homology Groups of Spaces of Nonsingular Algebraic Projective Hypersurfaces”, Proc. Steklov Inst. Math., 225 (1999), 121–140  mathnet  mathscinet  zmath
    4. V. A. Vassiliev, “Spaces of Hermitian operators with simple spectra and their finite-order cohomology”, Mosc. Math. J., 3:3 (2003), 1145–1165  mathnet  crossref  mathscinet  zmath
    5. V. A. Vassiliev, “Homology groups of spaces of non-resultant quadratic polynomial systems in ${\mathbb R}^3$”, Izv. Math., 80:4 (2016), 791–810  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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