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Monodromy and vanishing cycles of boundary singularities. (English. Russian original) Zbl 0591.32011
Funct. Anal. Appl. 19, 173-182 (1985); translation from Funkts. Anal. Prilozh. 19, No. 3, 11-21 (1985).
This paper deals with (skew-symmetric) monodromy groups for boundary critical points. In particular, the symplectic variants of Weyl groups $$B_{\mu}$$, $$C_{\mu}$$, $$F_ 4$$, $$G_ 2$$ are described, also, the vanishing cycles for $$B_{\mu}$$, $$C_{\mu}$$. Relations with monodromy groups of usual singularities are given.
Reviewer: N.Manolache

##### MSC:
 32S05 Local complex singularities 14B05 Singularities in algebraic geometry
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##### References:
 [1] V. I. Arnol’d, ”Critical points of functions on a manifold with boundary, the simple Lie groups Bk, Ck, F4 and singularities of evolutes,” Usp. Mat. Nauk,33, No. 5, 91-105 (1978). [2] V. I. Arnol’d, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Mappings, II [in Russian], Nauka, Moscow (1984). [3] A. N. Varchenko and S. V. Chmutov, ”Finite irreducible groups generated by reflections are monodromy groups of suitable singularities,” Funkts. Anal. Prilozhen.,18, No. 3, 1-13 (1984). · Zbl 0557.47005 · doi:10.1007/BF01076354 [4] S. M. Gusein-Zade, ”Monodromy groups of isolated singularities of hypersurfaces,” Usp. Mat. Nauk,32, No. 2, 23-65 (1977). · Zbl 0379.32013 [5] V. I. Arnol’d, ”Bifurcation of hyperelliptic integrals as functions of parameters,” Funkts. Anal. Prilozhen.,2, No. 3, 1-4 (1968). · Zbl 0174.45203 · doi:10.1007/BF01075356 [6] V. I. Arnol’d, ”Method of stationary phase and Coxeter numbers,” Usp. Mat. Nauk,28, No. 5, 17-44 (1973). [7] A. N. Varchenko, ”Bifurcation of multiple integrals, depending on parameters,” Funkts. Anal. Prilozhen.,3, No. 4, 79-80 (1969). · Zbl 0223.57006 · doi:10.1007/BF01078281 [8] A. M. Gabrielov, ”Intersection matrices for certain singularities,” Funkts. Anal. Prilozhen.,7, No. 3, 18-32 (1973). [9] A. M. Gabrielov, ”Dynkin diagrams of unimodal singularities,” Funkts. Anal. Prilozhen.,8, No. 3, 1-6 (1974). · Zbl 0294.47012 · doi:10.1007/BF02028300 [10] S. M. Gusein-Zade, ”Intersection matrices for certain singularities of functions of two variables,” Funkts. Anal. Prilozhen.,8, No. 1, 11-15 (1974). · Zbl 0304.14009 [11] S. M. Gusein-Zade, ”Dynkin diagrams for singularities of functions of two variables,” Funkts. Anal. Prilozhen.,8, No. 4, 23-30 (1974). · Zbl 0304.14009 [12] S. M. Gusein-Zade, ”Distinguished bases of simple singularities,” Funkts. Anal. Prilozhen.,14, No. 4, 73-74 (1980). [13] I. G. Shcherbak, ”Duality of boundary singularities,” Usp. Mat. Nauk,39, No. 2, 195-196 (1984). · Zbl 0581.58006 [14] S. V. Chmutov, ”Monodromy groups, singularities of functions of two variables,” Funkts. Anal. Prilozhen.,15, No. 1, 61-66 (1981). · Zbl 0464.51002 · doi:10.1007/BF01082383 [15] S. V. Chmutov, ”Monodromy groups of critical point of functions,” Invent. Math.,67, 123-131 (1982). · Zbl 0478.57022 · doi:10.1007/BF01393376 [16] S. V. Chmutov, ”Monodromy groups of critical point of functions. II,” Invent. Math.,73, 491-510 (1983). · Zbl 0536.32006 · doi:10.1007/BF01388441 [17] W. A. M. Janssen, ”Skew-symmetric vanishing lattices and their monodromy groups,” Ann. Math.,266, 115-133 (1983). · Zbl 0537.14005 · doi:10.1007/BF01458708 [18] B. Wajnrib, ”On the monodromy of plane curve singularities,” Ann. Math.,246, 141-154 (1980). · Zbl 0418.14017 · doi:10.1007/BF01420166 [19] N. A’Campo, ”Le group de monodromie du deploiement des singularites isolees de courbes planes,” Ann. Math.,213, 1-32 (1975). · Zbl 0316.14011 · doi:10.1007/BF01883883 [20] N. A’Campo, ”Tresses, monodromie et le groupe symplectique,” Commun. Math. Helv.,54, 318-327 (1979). · Zbl 0441.32004 · doi:10.1007/BF02566275 [21] A. M. Gabrielov, ”Polar curves and intersection matrices of singularities,” Invent. Math.,54, 15-22 (1979). · Zbl 0421.32011 · doi:10.1007/BF01391174 [22] W. Ebeling, ”On the monodromy groups of singularities,” Proc. Symp. Pure Math.,40, Part 1, 327-336 (1983). · Zbl 0518.32007 [23] V. I. Arnol’d, ”Singularities of systems of rays,” Usp. Mat. Nauk,38, No. 2, 77-147 (1983).
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