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Cohomology of Spaces of Complex Knots
Arnold Mathematical Journal. 2024. Vol. 10. No. 3. P. 323–353.
Cohomology groups of spaces of polynomial embeddings of the complex line to the complex space are studied
Vassiliev V., , in: Handbook of Geometry and Topology of Singularities VII.: Springer, 2025.
Classification of real function singularity and topological properties of the spaces of their singular and non-singular perturbations are described ...
Added: October 31, 2025
Vassiliev V., Israel Journal of Mathematics 2024 Vol. 263 P. 553-586
Isotopy classes of nnon-discriminant perturbations of simple function singularities are enumerated ...
Added: October 31, 2025
Vassiliev V., Moscow Mathematical Journal 2023 Vol. 23 No. 3 P. 401–432
The isotopy classes of non-discriminant perturbations of parabolic function singularities are listed ...
Added: October 31, 2025
Victor A. Vassiliev, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2020 Vol. 16 P. 1–21
Local diffusion of strictly hyperbolic higher-order PDE's with constant coefficients at all simple singularities of corresponding wavefronts can be explained and recognized by only two local geometrical features of these wavefronts. We radically disprove the obvious conjecture extending this fact to arbitrary singularities: namely, we present examples of diffusion at all non-simple singularity classes of generic wavefronts ...
Added: March 21, 2020
Victor A. Vassiliev, Journal of Knot Theory and Its Ramifications 2016 Vol. 25 No. 12
The construction of integer linking numbers of closed curves in a three-dimensional manifold usually appeals to the orientation of this manifold. We discuss how to avoid it constructing similar homotopy invariants of links in non-orientable manifolds. ...
Added: November 15, 2016
Esterov A. I., Advances in Mathematics 2013 Vol. 245 P. 534–572
Which polynomial in the coefficients of a system of algebraic equations should be called its discriminant? We prove a package of facts that provide a possible answer. Let us call a system typical, if the homeomorphic type of its set of solutions does not change as we perturb its (non-zero) coefficients. The set of all ...
Added: May 15, 2013
Esterov A. I., Discrete and Computational Geometry 2010 Vol. 44 No. 1 P. 96–148
For a system of polynomial equations, whose coefficients depend on parameters, the Newton polyhedron of its discriminant is computed in terms of the Newton polyhedra of the coefficients. This leads to an explicit formula (involving mixed fiber polyhedra and Euler obstructions of toric varieties) in the unmixed case, suggests certain open questions in general, and ...
Added: December 10, 2012