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@article{IM2_2016_80_4_a8, author = {V. A. Vassiliev}, title = {Homology groups of spaces of non-resultant quadratic polynomial systems in ${\mathbb R}^3$}, journal = {Izvestiya. Mathematics }, pages = {791--810}, publisher = {mathdoc}, volume = {80}, number = {4}, year = {2016}, language = {en}, url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_4_a8/} }
TY - JOUR AU - V. A. Vassiliev TI - Homology groups of spaces of non-resultant quadratic polynomial systems in ${\mathbb R}^3$ JO - Izvestiya. Mathematics PY - 2016 SP - 791 EP - 810 VL - 80 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_2016_80_4_a8/ LA - en ID - IM2_2016_80_4_a8 ER -
V. A. Vassiliev. Homology groups of spaces of non-resultant quadratic polynomial systems in ${\mathbb R}^3$. Izvestiya. Mathematics , Tome 80 (2016) no. 4, pp. 791-810. http://geodesic.mathdoc.fr/item/IM2_2016_80_4_a8/
[1] S. Smale, “Mathematical problems for the next century”, Math. Intelligencer, 20:2 (1998), 7–15 | DOI | MR | Zbl
[2] L. Blum, M. Shub, S. Smale, “On a theory of computation and complexity over the real numbers: $NP$-completeness, recursive functions and universal machines”, Bull. Amer. Math. Soc., 21:1 (1989), 1–46 | DOI | MR | Zbl
[3] M. Shub, S. Smale, “On the intractability of Hilbert's Nullstellensatz and an algebraic version of "$NP \neq P$?”, Duke Math. J., 81:1 (1995), 47–54 | DOI | MR | Zbl
[4] F. R. Cohen, R. L. Cohen, B. M. Mann, R. J. Milgram, “The topology of rational functions and divisors of surfaces”, Acta Math., 166:1 (1991), 163–221 | DOI | MR | Zbl
[5] A. Kozlowski, K. Yamaguchi, “Topology of complements of discriminants and resultants”, J. Math. Soc. Japan, 52:4 (2000), 949–959 | DOI | MR | Zbl
[6] V. A. Vassiliev, Complements of discriminants of smooth maps: topology and applications, Transl. Math. Monogr., 98, rev. ed., Amer. Math. Soc., Providence, RI, 1994, vi+208 pp. | MR | Zbl
[7] V. A. Vassiliev, “Homology of spaces of non-resultant homogeneous polynomial systems in $\mathbb R^2$ and $\mathbb C^2$”, Arnold Math. J., 1:3 (2015), 233–242 ; arXiv: 1409.6005 | DOI | MR | Zbl
[8] V. I. Arnol'd, “On some topological invariants of algebraic functions”, Trans. Moscow Math. Soc., 21, Amer. Math. Soc., Providence, RI, 1971, 30–52 | MR | Zbl
[9] A. Borel, J.-P. Serre, “Cohomologie d'immeubles et de groupes $s$-arithmétiques”, Topology, 15:3 (1976), 211–232 | DOI | MR | Zbl
[10] V. A. Vasilev, Topologiya dopolnenii k diskriminantam, M., Fazis, 1997, xiv+536 pp. | MR
[11] A. G. Gorinov, “Real cohomology groups of the space of nonsingular curves of degree 5 in $\mathbb{CP}^2$”, Ann. Fac. Sci. Toulouse Math. (6), 14:3 (2005), 395–434 ; arXiv: math/0105108 | DOI | MR | Zbl
[12] O. Tommasi, Geometry of discriminants and cohomology of moduli spaces, Dissertation, Radboud Universiteit, Nijmegen, 2005, 89 pp. \kern70pt\break http://repository.ubn.ru.nl/handle/2066/27027
[13] V. A. Vassiliev, “How to calculate homology groups of spaces of nonsingular algebraic projective hypersurfaces”, Proc. Steklov Inst. Math., 225 (1999), 121–140 ; arXiv: 1407.7229 | MR | Zbl
[14] A. Bahri, J. M. Coron, “On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain”, Comm. Pure Appl. Math., 41:3 (1988), 253–294 | DOI | MR | Zbl
[15] V. A. Vassiliev, “Stable cohomologies of the complements of the discriminants of deformations of singularities of smooth functions”, J. Soviet Math., 52:4 (1990), 3217–3230 | DOI | MR | Zbl
[16] V. A. Vassiliev, “Rational homology of the order complex of zero sets of homogeneous quadratic polynomial systems in $\mathbb R^3$”, Proc. Steklov Inst. Math., 290:1 (2015), 197–209 | DOI | DOI | Zbl
[17] S. Kallel, R. Karoui, “Symmetric joins and weighted barycenters”, Adv. Nonlinear Stud., 11:1 (2011), 117–143 ; arXiv: math/0602283v3 | DOI | MR | Zbl
[18] J.-P. Serre, “Homologie singulière des espaces fibrés. Applications”, Ann. of Math. (2), 54:3 (1951), 425–505 | DOI | MR | MR | Zbl | Zbl
[19] A. Borel, “Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts”, Ann. of Math. (2), 57 (1953), 115–207 | DOI | MR | MR | Zbl | Zbl
[20] V. A. Vasil'ev, “Homology of spaces of homogeneous polynomials in $\mathbf R^2$ without multiple zeros”, Proc. Steklov Inst. Math., 221 (1998), 133–138 ; arXiv: 1407.7230 | MR | Zbl