18 citations · 51 across the 30 of their papers we have counts for
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Homology groups of spaces of non-resultant quadratic polynomial systems in R^3
Victor A. Vassiliev
We calculate rational homology groups of spaces of non-resultant (i.e. having no non-trivial common zeros) systems of homogemeous quadratic polynomials in R^3
Homology of spaces of non-resultant polynomial systems in R^2 and C^2
V. A. Vassiliev
The resultant veriety in the space of systems of homogeneous polynomials of given degrees consists of such systems having non-trivial solutions. We calculate the integer cohomology…
Complexes of connected graphs
V. A. Vassiliev
Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applica…
Monodromy of complete intersections and surface potentials
Victor A. Vassiliev
Following Newton, Ivory and Arnold, we study the Newtonian potentials of algebraic hypersurfaces in . The ramification of (analytic continuations of) these potential depends o…
On -neighborly submanifolds in
Victor A. Vassiliev
A submanifold is -neighborly if for any points in there is a hyperplane, supporting and touching it at exactly these points. We prove that the mi…
Spaces of Hermitian operators with simple spectra and their finite-order cohomology
Victor A. Vassiliev
The topology of spaces of Hermitian operators in with non-simple spectra was studied by V.Arnold in a relation with the theory of adiabatic connections and the quantum Hall e…
Topology of plane arrangements and their complements
Victor A. Vassiliev
This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, strati…
On combinatorial formulas for cohomology of spaces of knots
Victor A. Vassiliev
We develop homological techniques for finding explicit combinatorial expressions of finite-type cohomology classes of spaces of knots in generalizing Polyak--Viro f…
Stratified Picard-Lefschetz Theory with Twisted Coefficients
Victor A. Vassiliev
The monodromy action in the homology (generally with twisted coefficients) of complements of stratified complex analytic varieties depending on parameters is studied. For a wide cl…
Homology of spaces of homogeneous polynomials in without multiple zeros
Victor A. Vassiliev
For any natural we calculate the cohomology groups of the space of homogeneous polynomials of degree , which do not vanish with multiplicity …
How to calculate homology groups of spaces of nonsingular algebraic projective hypersurfaces
Victor A. Vassiliev
A general method of computing cohomology groups of the space of nonsingular algebraic hypersurfaces of degree in is described. Using this method, rational cohomology gro…
On Finite Order Invariants of Triple Points Free Plane Curves
Victor A. Vassiliev
We describe some regular techniques of calculating finite degree invariants of triple points free smooth plane curves . They are a direct analog of similar techniques…
There are no algebraically integrable ovals in even-dimensional spaces
Victor A. Vassiliev
We prove that there are no bounded domains with smooth boundaries in even-dimensional Euclidean spaces, such that the volumes cut off from them by affine hyperplanes depend algebra…