Related papers: Triod twist cycles and circle rotations
The notion of constant cycle curves on K3 surfaces is introduced. These are curves that do not contribute to the Chow group of the ambient K3 surface. Rational curves are the most prominent examples. We show that constant cycle curves…
Several cycle lexicographical orders are found to describe the relative likelihood of elements of the random walks on the symmetric group generated by the conjugacy classes of transpositions, 3-cycles, and n-cycles. Spectral analysis finds…
We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain…
We solve some computational problems for triangulated closed three-dimensional manifolds using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms for computing the intersection numbers of 1- and 2-dimensional…
In this paper, we prove a tight minimum degree condition in general graphs for the existence of paths between two given endpoints, whose lengths form a long arithmetic progression with common difference one or two. This allows us to obtain…
In this paper we consider non-singular Morse-Smale flows on closed orientable 3-manifolds, under the assumption that among the periodic orbits of the flow there is only one saddle orbit and it is twisted. It is found that any manifold…
The stable Andrews-Curtis conjecture in combinatorial group theory is the statement that every balanced presentation of the trivial group can be simplified to the trivial form by elementary moves corresponding to "handle-slides" together…
In this paper we answer positively a question of whether it is possible for a circle diffeomorphism with breaks to be smoothly conjugate to a rigid rotation in the case when its breaks are lying on pairwise distinct trajectories. An example…
In \cite{striker2018rowmotion} Striker generalized Cameron and Fon-Der-Flaass's notion of a toggle group. In this paper we begin the study of transitive generalized toggle groups that contain a cycle. We first show that if such a group has…
This is one of a series of articles, in collaboration with C. Moeglin, whose goal is to stabilize the twisted trace formula. In the previous article, we have stated several assertions about the stabilization of weighted orbital integrals…
We introduce and study a complexity function on words $c_x(n),$ called \emph{cyclic complexity}, which counts the number of conjugacy classes of factors of length $n$ of an infinite word $x.$ We extend the well-known Morse-Hedlund theorem…
In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic…
The topology of the orbit space, $Y$, for the action of the complex conjugation on a complex surface, $X$, defined over reals, is studied. I give a criterion for blow-up stable triviality of $Y$ (which implies vanishing of its…
In this paper, we explore minimal contact triangulations on contact 3-manifolds. We give many explicit examples of contact triangulations that are close to minimal ones. The main results of this article say that on any closed oriented…
The conjugacy problem in braid groups has been extensively studied, particularly from an algorithmic perspective. Established methods based on Garside structures, such as initial summit sets and super summit sets, provide effective…
We investigate rational maps with period one and two cluster cycles. Given the definition of a cluster, we show that, in the case where the degree is $d$ and the cluster is fixed, the Thurston class of a rational map is fixed by the…
For a given pair of numbers $(d,k)$, we establish the minimal number of vertices in pure $d$-dimensional simplicial complexes with non-trivial homology in dimension $k$. Furthermore, we solve the problem under the additional constraint of…
We describe explicitly the cohomology of the total complex of certain diagrams of invertible sheaves on normal toric varieties. These diagrams, called wheels, arise in the study of toric singularities associated to dimer models. Our main…
Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra…
We completely determine the free parts of the set-theoretic Yang-Baxter (co)homology groups of finite cyclic biquandles, along with fully computing the torsion subgroups of their 1st and 2nd homology groups. Furthermore, we provide upper…