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Mat. Zametki, 1969, Volume 5, Issue 2, Pages 227–231 (Mi mz6827)  

This article is cited in 20 scientific papers (total in 21 papers)

The cohomology ring of the colored braid group

V. I. Arnol'd

M. V. Lomonosov Moscow State University

Abstract: The cohomology ring is obtained for the space of ordered sets of $n$ different points of a plane.

Full text: PDF file (360 kB)

English version:
Mathematical Notes, 1969, 5:2, 138–140

Bibliographic databases:

UDC: 513.83
Received: 29.04.1968

Citation: V. I. Arnol'd, “The cohomology ring of the colored braid group”, Mat. Zametki, 5:2 (1969), 227–231; Math. Notes, 5:2 (1969), 138–140

Citation in format AMSBIB
\Bibitem{Arn69}
\by V.~I.~Arnol'd
\paper The cohomology ring of the colored braid group
\jour Mat. Zametki
\yr 1969
\vol 5
\issue 2
\pages 227--231
\mathnet{http://mi.mathnet.ru/mz6827}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=242196}
\zmath{https://zbmath.org/?q=an:0277.55002}
\transl
\jour Math. Notes
\yr 1969
\vol 5
\issue 2
\pages 138--140
\crossref{https://doi.org/10.1007/BF01098313}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. M. Gel'fand, A. V. Zelevinskii, “Algebraic and combinatorial aspects of the general theory of hypergeometric functions”, Funct. Anal. Appl., 20:3 (1986), 183–197  mathnet  crossref  mathscinet  zmath  isi
    2. A. N. Varchenko, I. M. Gel'fand, “Heaviside functions of a configuration of hyperplanes”, Funct. Anal. Appl., 21:4 (1987), 255–270  mathnet  crossref  mathscinet  zmath  isi
    3. V. A. Vassiliev, “Braid group cohomologies and algorithm complexity”, Funct. Anal. Appl., 22:3 (1988), 182–190  mathnet  crossref  mathscinet  zmath  isi
    4. V. A. Golubeva, V. P. Leksin, “Quadratic Relations in the Cohomology of Generalized Pure Braids and Dunkl Identities”, Funct. Anal. Appl., 30:2 (1996), 131–134  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. D. V. Anosov, A. A. Bolibrukh, V. A. Vassiliev, A. M. Vershik, A. A. Gonchar, M. L. Gromov, S. M. Gusein-Zade, V. M. Zakalyukin, Yu. S. Ilyashenko, V. V. Kozlov, M. L. Kontsevich, Yu. I. Manin, A. I. Neishtadt, S. P. Novikov, Yu. S. Osipov, M. B. Sevryuk, Ya. G. Sinai, A. N. Tyurin, L. D. Faddeev, B. A. Khesin, A. G. Khovanskii, “Vladimir Igorevich Arnol'd (on his 60th birthday)”, Russian Math. Surveys, 52:5 (1997), 1117–1139  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    6. V. V. Vershinin, E. Ossa, “The Thom Spectra of the Commutator Subgroups of the Generalized Braid Groups”, Funct. Anal. Appl., 32:4 (1998), 219–226  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. V. V. Vershinin, “Braid groups and loop spaces”, Russian Math. Surveys, 54:2 (1999), 273–350  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. V. M. Buchstaber, T. E. Panov, “Torus actions, combinatorial topology, and homological algebra”, Russian Math. Surveys, 55:5 (2000), 825–921  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. V. A. Vassiliev, “Topology of plane arrangements and their complements”, Russian Math. Surveys, 56:2 (2001), 365–401  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Vassiliev, VA, “Homology of spaces of knots in any dimensions”, Philosophical Transactions of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 359:1784 (2001), 1343  crossref  isi
    11. J. Damon, “On the legacy of free divisors. II. Free* divisors and complete intersections”, Mosc. Math. J., 3:2 (2003), 361–395  mathnet  mathscinet  zmath  elib
    12. V. É. Turchin, “What is one-term relation for higher homology of long knots”, Mosc. Math. J., 6:1 (2006), 169–194  mathnet  mathscinet  zmath
    13. Callegaro, F, “The homology of the Milnor fiber for classical braid groups”, Algebraic and Geometric Topology, 6 (2006), 1903  crossref  isi
    14. Tourtchine V., “On the other side of the bialgebra of chord diagrams”, Journal of Knot Theory and Its Ramifications, 16:5 (2007), 575–629  crossref  isi
    15. Brown, FCS, “MULTIPLE ZETA VALUES AND PERIODS OF MODULI SPACES (m)over-bar(0,n)”, Annales Scientifiques de l Ecole Normale Superieure, 42:3 (2009), 371  isi
    16. V. P. Leksin, “Topology of Complements of Hyperplane Arrangements and Isomonodromic Deformations of Fuchsian Systems”, Proc. Steklov Inst. Math., 267 (2009), 190–194  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    17. V. P. Leksin, “Multidimensional Jordan–Pochhammer systems and their applications”, Proc. Steklov Inst. Math., 278 (2012), 130–138  mathnet  crossref  mathscinet  isi  elib  elib
    18. Yury Neretin, “On topologies on Malcev completions of braid groups”, Mosc. Math. J., 12:4 (2012), 803–824  mathnet  mathscinet
    19. Church T., Farb B., “Representation Theory and Homological Stability”, Adv. Math., 245 (2013), 250–314  crossref  isi
    20. Anatol N. Kirillov, “On Some Quadratic Algebras I $\frac{1}{2}$: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss–Catalan, Universal Tutte and Reduced Polynomials”, SIGMA, 12 (2016), 002, 172 pp.  mathnet  crossref
    21. Darij Grinberg, “$t$-Unique Reductions for Mészáros's Subdivision Algebra”, SIGMA, 14 (2018), 078, 34 pp.  mathnet  crossref
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