arXiv research

Characterizes quasi-isometric embeddings in coarsely Lipschitz category.

We prove that a monomorphic functor $F:Comp\to Comp$ with finite supports is epimorphic, continuous, and its maximal $\emptyset$-modification $F^\circ$ preserves intersections. This implies that a monomorphic functor $F:Comp\to Comp$ of finite degree $deg F\le n$ preserves (finite-dimensional) compact ANR's if the spac…

There are well-known monomorphisms between the Artin groups of finite type $\arA_n$, $\arB_n=\arC_n$ and affine type $\tilde \arA_{n-1}$, $\tilde\arC_{n-1}$. The Artin group $A(\arA_n)$ is isomorphic to the $(n+1)$-strand braid group $B_{n+1}$, and the other three Artin groups are isomorphic to some subgroups of $B_{n+…

Wright showed that, if a 1-ended simply connected locally compact ANR Y with pro-monomorphic fundamental group at infinity admits a proper Z-action, then that fundamental group at infinity can be represented by an inverse sequence of finitely generated free groups. Geoghegan and Guilbault strengthened that result, prov…

Suppose that $M$ is a connected orientable $n$-dimensional manifold and $m>2n$. If $H^i(M,\R)=0$ for $i>0$, it is proved that for each $m$ there is a monomorphism $H^m(W_n,\on{O}(n))\to H^m_{\on{cont}}(\on{Diff}M,\R)$. If $M$ is closed and oriented, it is proved that for each $m$ there is a monomorphism $H^m(W_n,\on{O}…

A. Borel proved that, if a finite group $F$ acts effectively and continuously on a closed aspherical manifold $M$ with centerless fundamental group $π_1(M)$, then a natural homomorphism $ψ$ from $F$ to the outer automorphism group ${\rm Out} π_1(M)$ of $π_1(M)$, called the associated abstract kernel, is a monomorphism.…

In 1992, David Wright proved a remarkable theorem about which contractible open manifolds are covering spaces. He showed that if a one-ended open manifold M has pro-monomorphic fundamental group at infinity which is not pro-trivial and is not stably Z, then M does not cover any manifold (except itself). In the non-mani…

Aim of this note is to extract cohomological information about the manifold $Emb(M,N)$ from the topology of the target manifold N. For special conditions, a monomorphism $H^1 (N) \to H^1 (Emb(M,N))$ is constructed.

Let F be a non-abelian finite rank free group, and let H_g be the fundamental group of a surface of genus g with one boundary component represented by D_g in H_g. So, H_g is the free group <a_1,b_1,...,a_g,b_g> and D_g is the product of commutators [a_1,b_1]...[a_g,b_g]. Given x in F, we are interested in the number nu…

The equivariant Gromov--Hausdorff convergence of metric spaces is studied. Where all isometry groups under consideration are compact Lie, it is shown that an upper bound on the dimension of the group guarantees that the convergence is by Lie homomorphisms. Additional lower bounds on curvature and volume strengthen this…

Study presentations of groups that can be generalised over continuous open group monomorphisms.

We prove that groups that are mod-p-homology equivalent are isomorphic modulo any term of their derived p-series, in precise analogy to Stallings' 1963 result for the lower-central p-series. Similarly spaces that are mod-p-homology equivalent have fundamental groups that are isomorphic modulo any term of their p-derive…

In~\cite{Ma} Manturov studied groups $G_{n}^{k}$ for fixed integers $n$ and $k$ such that $k<n$. In particular, $G_{n}^{2}$ is isomorphic to the group of free braids of $n$-stands. In~\cite{KiMa} Manturov and the author studied an invariant valued in free groups not only for free braids but also for free tangles, which…

We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on mapping class groups of once-punctured surfaces and have quite curious behaviour…

In the present paper, we construct a monomorphism from (Artin) pure braid group $PB_{n}$ into a group, which is `bigger' than $PB_{n}$. Roughly speaking, this mapping is defined on words of braids by adding `new generators' between generators of $PB_{n}$. By this mapping we can get a new invariant for classical braids.…

Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to the inverse braid monoids. Namely we prove an inclusion into a monoid of partial m…

Two graph homologies help compute embedding space.

Finite subgroups of good groups correspond to their profinite completions.

A Polish group $G$ is called a group of quasi-invariance or a QI-group, if there exist a locally compact group $X$ and a probability measure $μ$ on $X$ such that 1) there exists a continuous monomorphism of $G$ to $X$, and 2) for each $g\in X$ either $g\in G$ and the shift $μ_g$ is equivalent to $μ$ or $g\not\in G$ and…

For a smooth (locally trivial) principal bundle in Ehresmann's sense, the relation between the commuting vertical and horizontal actions of the structural Lie group and the structural Lie groupoid (isomorphisms between vertical fibers) is regarded as a special case of a symmetrical concept of conjugation between "princ…

The paper studies geodesic hypersurfaces in hyperbolic manifolds and their fundamental groups.

This research classifies deformations of Yang-Baxter operators using cohomology of $n$-Lie algebras.

The leverage effect refers to the generally negative correlation between the return of an asset and the changes in its volatility. There is broad agreement in the literature that the effect should be present for theoretical reasons, and it has been consistently found in empirical work. However, a few papers have pointe…

New method for interpreting non-linear models using forward marginal effects.

The Kalinin effectivity is studied and applied to compactifications and Hilbert squares.

New method estimates treatment effects in network data, accounting for spillover effects.

Causalfe estimates treatment effects in panel data with fixed effects.

The paper clarifies the distinction between CATE and ITE under ignorability assumptions.

GADGET framework decomposes global feature effects using recursive partitioning.

A new RL framework evaluates dynamic mediation effects over time.

New memory effect discovered in gravitational wave behavior.

Effective Yau-Tian-Donaldson conjecture for spherical varieties.

A new method estimates treatment effects in mixed groups, improving accuracy.

Study estimates heterogeneous principal causal effects with binary treatments and intermediate variables.

Study develops method for estimating causal effects in continuous variables.

ICA accurately estimates treatment effects even with confounders.

Method improves treatment effect estimation in randomized experiments.

New method discovers context effects in choice data.

Dropout introduces both explicit and implicit regularization effects.

New test for binary treatment effects using kernel methods.

New Krylov subspace methods speed up mixed-effects models with crossed random effects.

The use of drug combinations, termed polypharmacy, is common to treat patients with complex diseases and co-existing conditions. However, a major consequence of polypharmacy is a much higher risk of adverse side effects for the patient. Polypharmacy side effects emerge because of drug-drug interactions, in which activi…

Previous literature has identified an effect, dubbed the Zumbach effect, that is nonzero empirically but conjectured to be zero in any conventional stochastic volatility model. Essentially this effect corresponds to the property that past squared returns forecast future volatilities better than past volatilities foreca…

Identifies causal effects in LiNGAM models with latent variables.

Develops HCQRF for estimating heterogeneous treatment effects with censored data.

Study relaxes identification assumptions for natural direct effects in non-randomized settings.

The Sagnac effect is re-examined using Finslerian geometry.

We study the relationship between national culture and the disposition effect by investigating international differences in the degree of investors' disposition effect. We utilize brokerage data of 387,993 traders from 83 countries and find great variation in the degree of the disposition effect across the world. We fi…