arXiv research

Study stabilizes components of Galois cover moduli spaces.

CCCDs tackle class imbalance in classification.

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Infere…

The paper studies liftable mapping class groups of cyclic covers of spheres.

Study mapping class group action on cohomology of SL_n character variety.

Closed self-covering manifolds with abelian fundamental groups fiber over tori.

Study of Dehn twists on a disc with 3 points, solving conjugacy problem.

We study elliptic theory on manifolds with boundary represented as a covering space. Firstly, we consider boundary value problems, where the boundary conditions are allowed to mix the values of functions in the fibers of the covering. We show that elliptic elements define Fredholm operators and prove an index formula. …

We prove that the canonical 4-dimensional surgery problems can be solved after passing to a double cover. This contrasts the long-standing conjecture about the validity of the topological surgery theorem for arbitrary fundamental groups (without passing to a cover). As a corollary, the surgery conjecture is reformulate…

New examples show transverse knots are determined by their branched covers.

This paper concerns the class of contractible open 3-manifolds which are ``locally finite strong end sums'' of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of another 3-manifold the group of covering translations must be a free group. It follow…

We say that a cover of surfaces S -> X has the Birman--Hilden property if the subgroup of the mapping class group of X consisting of mapping classes that have representatives that lift to S embeds in the mapping class group of S modulo the group of deck transformations. We identify one necessary condition and one suffi…

Odd covers have one Anosov flow, even covers have two.

New braid group representations into mapping class groups are derived from disk coverings.

The study explores how the mapping class group acts on the homology of surface covers.

The diameter function is a topological Morse function.

Study of fundamental groups of 3D small covers using Morse theory.

We investigate the filling area conjecture, optimal systolic inequalities, and the related problem of the nonvanishing of certain linking numbers in 3-manifolds.

Study of lifting maps in branched covers of 3-manifolds, showing non-injectivity.

The paper presents a chain complex for 3-manifold covers, including surface bundles and surgeries.

An oriented connected closed manifold $M^n$ is called a URC-manifold if for any oriented connected closed manifold $N^n$ of the same dimension there exists a nonzero degree mapping of a finite-fold covering $\widehat{M}^n$ of $M^n$ onto $N^n$. This condition is equivalent to the following: For any $n$-dimensional integ…

Nonorientable surface mapping class group embeds quasi-isometrically in its orientable cover.

We show that if $F$ is a convex class of functions that is $L$-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages. To that end, we establish new sharp upper and lower e…

Based on the analogy between knots and primes, J. Hillman, D. Matei and M. Morishita defined the Iwasawa invariants for sequences of cyclic covers of links with an analogue of Iwasawa's class number formula of number fields. In this paper, we consider the existence of covers of links with prescribed Iwasawa invariants,…

The Birman-Hilden theory is extended to infinite type surfaces and branched covers.

Study mapping class groups of cyclic covers, focusing on liftability.

In this paper we calculate the number of equivariant diffeomorphism classes of small covers over a prism.

In the present paper we find a bijection between the set of small covers over an $n$-cube and the set of acyclic digraphs with $n$ labeled nodes. Using this, we give a formula of the number of small covers over an $n$-cube (generally, a product of simplices) up to Davis-Januszkiewicz equivalence classes and $\mathbf{Z}…

In this paper we show that for m>n the set of cobordism classes of maps from m-sphere to n-sphere is trivial. The determination of the cobordism homotopy groups of spheres admits applications to the covers for spheres.

Analogue of classical Hurwitz numbers is defined in the work for regular coverings of surfaces with marked points by seamed surfaces. Class of surfaces includes surfaces of any genus and orientability, with or without boundaries; coverings may have certain singularities over the boundary and marked points. Seamed surfa…

Proves conjecture about surface cover homology.

New algorithm reduces prediction error in online learning without knowing base measure.

This paper solves a problem in 3D geometry by defining a canonical partition for certain manifolds.

Compactifies the space of branched coverings of the sphere.

Develops algorithm for finite generating set of liftable mapping class groups of regular abelian covers.

The paper explores subrepresentations in graph homology.

We show that every strongly-cyclic branched covering of a (1,1)-knot is a Dunwoody manifold. This result, together with the converse statement previously obtained by Grasselli and Mulazzani, proves that the class of Dunwoody manifolds coincides with the class of strongly-cyclic branched coverings of (1,1)-knots. As a c…

Let $Σ$ be a surface whose interior admits a hyperbolic structure of finite volume. In this paper, we show that any infinite order mapping class acts with infinite order on the homology of some universal $k$--step nilpotent cover of $Σ$. We show that a Torelli mapping class either acts with infinite order on the homolo…

We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1,1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold strongly-cyclic branched coverings of (1,1)-knots, thro…

In the 1970s Joan Birman and Hugh Hilden wrote several papers on the problem of relating the mapping class group of a surface to that of a cover. We survey their work, give an overview of the subsequent developments, and discuss open questions and new directions.

Non-orientable 4-manifolds are simple branched coverings of RP^4 and twisted S^3-bundles.

Study graded coverings for supermanifolds, proving their universal properties.

A new method using mod n covering improves systolic inequalities.

Study homology groups of mapping and Torelli groups for surfaces with abelian covers.

We solve the isomorphism problem for the whole class of Lins-Mandel gems (graphs encoded manifolds). We also present certain homeomorphisms of branched cyclic coverings of two-bridge hyperbolic links. As a consequence, we prove that, in in a wide subset of interesting cases, the isomorphism conditions for Lins-Mandel g…

Study shows certain knots can't be sliced using 2-fold branched covers.

Generative adversarial approach for satellite image time series land cover classification.

We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are not concave. We provide conditions under which a maximizer exists. The class of …