arXiv research

Investigates local indicability of groups with circle homology presentations.

Extends coherence results to one-relator products of locally indicable groups.

Generalizes Collins' theorem to products of locally indicable groups.

The paper shows how reducible complexes affect local indicability.

By the Thurston stability theorem, a group of C^1 orientation-preserving diffeomorphisms of the closed unit interval is locally indicable. We show that the local order structure of orbits gives a stronger criterion for nonsmoothability that can be used to produce new examples of locally indicable groups of homeomorphis…

Twists agrarian and $\ell^2$-Betti numbers for locally indicable groups.

We study a class of localized indices for the Dirac type operators on a complete Riemannian orbifold, where a discrete group acts properly, co-compactly and isometrically. These localized indices, generalizing the $L^2$-index of Atiyah, are obtained by taking certain traces of the higher index for the Dirac type operat…

According to Thurston's stability theorem, every group of C^1 diffeomorphisms of the closed interval is locally indicable (.e., every finitely generated subgroup factors through Z). We show that, even for finitely generated groups, the converse of this statement is not true. More precisely, we show that the semi-direct…

The study characterizes elements of a group quotient and finds a non-locally indicable left-orderable group.

In this paper, we investigate topological aspects of indices of twisted geometric operators on manifolds equipped with fibered boundaries. We define $K$-groups relative to the pushforward for boundary fibration, and show that indices of twisted geometric operators, defined by complete $Φ$ or edge metrics, can be regard…

Strict concavity proven for growth indicator function of certain groups.

The study provides bounds for geodesic diameter in Euclidean space.

New composite indicators reveal hidden relationships between indicators.

The paper describes the structure of injective LOT-complexes and proves they are aspherical.

This study examined how the correlation and network structure of 30 global indices and 145 local Korean indices belonging to the KOSPI 200 have changed during the 13-year period, 2000-2012. The correlations among the indices were calculated. The results showed that although the average correlations of the global indice…

This paper introduces an intersection theory problem for maps into a smooth manifold equipped with a stratification. We investigate the problem in the special case when the target is the unitary group and the domain is a circle. The first main result is an index theorem that equates a global intersection index with a f…

We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest ei…

Let G be a group and let O_G denote the set of left orderings on G. Then O_G can be topologized in a natural way, and we shall study this topology to answer three conjectures. In particular we shall show that O_G can never be countably infinite. Furthermore in the case G is a countable nonabelian free group, we shall s…

Let Gamma be a finitely generated, amenable group. Using an idea of E Ghys, we prove that if Gamma has a nontrivial, orientation-preserving action on the real line, then Gamma has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Gamma has a faithful action on the circle, then some finite-in…

Study index theory on Lie group homogeneous spaces using topological and analytic methods.

We present a new test for studying asphericity and diagrammatic reducibility of group presentations. Our test can be applied to prove diagrammatic reducibility in cases where the classical weight test fails. We use this criterion to generalize results of J. Howie and S.M. Gersten on asphericity of LOTs and of Adian pre…

This is a draft of a book submitted for publication by the AMS. Its theme is the remarkable interplay, accelerating in the last few decades, between topology and the theory of orderable groups, with applications in both directions. It begins with an introduction to orderable groups and their algebraic properties. Many …

LoBoost improves local conformal prediction for gradient-boosted trees without extra data splits.

Indices of vector fields and 1-forms studied for singular varieties and actions.

We study the dynamic interactions and structural changes in global financial indices in the years 1998-2012. We apply a principal component analysis (PCA) to cross-correlation coefficients of the stock indices. We calculate the correlations between principal components (PCs) and each asset, known as PC coefficients. A …

Anosov groups limit sets are Ahlfors regular, with applications in Teichmüller spaces.

We define two types of local indices of a vector field at an isolated zero on the boundary, and prove Poincare-Hopf-type index theorems for certain vector fields on a compact smooth manifold which have only isolated zeros.

Compact leaves with amenable groups are stable under small perturbations.

New indices defined for manifolds with boundary, generalizing previous results.

Paper calculates indices for group actions using cocycles.

The paper extends a theorem to number fields without infinite places.

Simon's knot genus problem solved with 3-manifold groups.

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic…

Develops a new theory of localization in algebraic geometry.

Gradient boosting predicts promotion efficiency using multiple performance indicators.

I present a selection of results on locally conformally Kähler geometry published after 1997. The proofs are mainly sketched, some of them are even omitted. Several open problems are indicated in the end.

Generically an almost complex structure has no symmetries at all, but there exist symmetric structures. In this paper we describe how to guarantee that the pseudogroup of local symmetries is small (finite-dimensional). It will be indicated that a large symmetry pseudogroup (infinite-dimensional) is a signature of some …

We introduce a new measure for the capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term and short-term memory) and local herding behavior (fractal dimension). The efficiency measure is taken as a distance from an ideal efficient market situation. Methodolog…

Study fixed point indices and words at infinity for graph selfmaps.

Study of quasimorphisms and bounded cohomology in braided Thompson groups.

The paper develops techniques to study entropy and rigidity in RCD-spaces.

Study examines how industrial emissions evolve over time in response to various factors.

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups whic…

Paper disproves a Smith conjecture about sphere actions.

The study calculates braid indices for two-bridge knots and proves inequalities.

Study on rational projective planes with small index singularities.

Every locally compact local group is locally isomorphic to a topological group.

Study of invariants on manifolds with boundary involving equivariant spectral flow and η-invariants.