?
Twisted homology of configuration spaces and homology of spaces of equivariant maps
Doklady Mathematics (Springer, Germany). 2018. Vol. 98. No. 3. P. 629–633.
We calculate homology groups with certain twisted coefficients of configuration spaces of projective spaces. This completes a calculation of rational homology groups of spaces of odd maps of spheres S^m \to S^M, m<M, and of the stable homology of spaces of non-resultant polynomial maps R^{m+1} -> R^{M+1}. Also, we calculate the homology of spaces of Z_r-equivariant maps of odd-dimensional spheres, and discuss further generalizations.
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Vassiliev V., Homology, Homotopy and Applications 2024 Vol. 26 No. 2 P. 219–227
The rational cohomology ring of the space of maps of spheres equivariant under the Hopf action of the circle is isomorphic to that of a complex Stiefel manifold ...
Added: October 31, 2025
Vassiliev V., Journal of Topology and Analysis 2024 Vol. 16 No. 4 P. 461–494
A general method of computing the cohomology groups of spaces of equivariant maps is developed and applied to the spaces of odd and even maps of spheres ...
Added: October 31, 2025
Vassiliev V., Pacific Journal of Mathematics 2023 Vol. 326 No. 1 P. 135–160
The topology of the space of subalgebras of the function space specified by collections of equality conditins f(x)=f(y) is studied and applied to the problems of interpolation theory and knot theory ...
Added: October 31, 2025
Khoroshkin A., Lyskov D., / Series math "arxiv.org". 2025.
Added: October 14, 2025
V.A.Vassiliev, European Journal of Combinatorics 2020 Vol. 86 P. 1–7
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of Goresky–MacPherson approach to similar homology calculations is proposed. ...
Added: March 21, 2020
V.A.Vassiliev, Doklady Mathematics 2018 Vol. 98 No. 1 P. 330–333
Stable rational cohomology groups of spaces of non-resultant homogeneous polynomial systems of growing degree in R^n are calculated ...
Added: December 7, 2018
В.А.Васильев, Известия РАН. Серия математическая 2016 Т. 80 № 4 С. 163–184
Rational homology groups of spaces of non-resultant (that is, having only trivial common zeros) systems of homogeneous quadratic polynomial systems in R^3 are calculated ...
Added: March 3, 2018
Flores R., Ivanou A., Social Movement Studies 2018 P. 1–16
This paper develops Bourdieusian notions of habitus, capital and field, along with the allied concepts of hysteresis and homology, to examine routes into public activism in post-Soviet Russia. Focusing on a neighbourhood campaign against construction projects in the Moscow district of Izmailovo, we argue that mobilization was driven by activists whose formative years took place ...
Added: January 17, 2018
Vassiliev V., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2017 Т. 477 № 6 С. 637–640
The stabilization of cohomology rings of spaces of non-resultant homogeneous polynomial systems of growing degree in $\R^3$ is studied. The rational stable cohomology rings are explicitly calculated, and the instant of stabilization is estimated ...
Added: December 27, 2017