Related papers: A characterization of alternating link exteriors i…
We describe when two multiprojective bundles (fibre products of projective bundles over the same base) over projective spaces are isomorphic as abstract varieties. We also describe when two relative symmetric powers of projective bundles…
In this article we study the construction of characteristic classes for principal $G$-bundles equipped with an additional structure called transitionally commutative structure (TC structure). These structures classify, up to homotopy,…
We consider an algebra of (classical or virtual) tangles over an ordered circuit operad and introduce Conway-type invariants of tangles which respect this algebraic structure. The resulting invariants contain both the coefficients of the…
In this paper, we consider a special kind of overconstrained 6R closed linkages which we call angle-symmetric 6R linkages. These are linkages with the property that the rotation angles are equal for each of the three pairs of opposite…
A Divide with cusps is the image of a proper generic immersion from finite intervals and circles into a $2$-disk which allows to have cusps. A divide with cusps is the generalization of the notion of the divide which is introduced by…
We investigate several topological and combinatorial properties of line arrangements. We associate to a line arrangement a link obtained by intersecting the arrangement with some sphere. Several topics are discussed: (a) some link…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
Signed network embedding is an approach to learn low-dimensional representations of nodes in signed networks with both positive and negative links, which facilitates downstream tasks such as link prediction with general data mining…
We describe a construction (the `warped cone construction') which produces examples of coarse spaces with large groups of translations. We show that by this construction we can obtain many examples of coarse spaces which do not have…
We describe the additive subgroups of fields which are closed with respect to taking inverses. In particular, in characteristic different from two any such subgroup is either a subfield or the kernel of the trace map of a quadratic…
A linear system of real quadratic forms defines a real projective variety. The real non-singular locus of this variety (more precisely of the underlying scheme) has a highly connected double cover as long as each non-zero form in the system…
Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these…
We present a study of cubic surfaces from the novel perspective of positive geometry. Our positive geometries have dimension two (the surface minus its 27 lines), dimension three (its complement in 3-space), and dimension four (the moduli…
We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.
The flurry of theoretical and experimental studies following the report of room-temperature superconductivity at ambient pressure in Cu-substituted lead apatite Cu$_x$Pb$_{10-x}$(PO$_4$)$_6$O (`LK99') have explored whether and how this…
We generalize Hansen--Strobl's definition of $H$-twisted Courant algebroid such that the twist $H$ of the Jacobi identity is a 4-form in the kernel of the anchor map and is closed under a naturally occurring exterior covariant derivative.…
We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a…
We classify the automorphisms of a Moufang hexagon mapping no chamber to an opposite chamber (such automorphisms are called domestic). This forms part of a larger program to classify domestic automorphisms of Moufang spherical buildings.
Binary multirelations form a model of alternating nondeterminism useful for analysing games, interactions of computing systems with their environments or abstract interpretations of probabilistic programs. We investigate this alternating…
We construct configuration spaces for cyclic covers of the projective line that admit extra automorphisms and we describe the locus of curves with given automorphism group. As an application we provide examples of arbitrary high genus that…