arXiv research

We analyze oversquashing in topological message-passing using relational structures.

Survey on hyperplane arrangements and their topology.

The abstract explains counterexamples in 4-manifold topology.

Homflypt skein theory and string topology linked via 2-groupoids.

Studies amenable category's monotonicity and its relation to topological complexity.

Stability of mapping spaces is shown to be related to the D-topology.

TDL uses topological features for deep learning models, promising new insights and solutions.

Lectures on mean curvature flow and its related equations.

Survey on geometry and topology of maximal antipodal sets.

Develops a braid-theoretic framework to analyze chirality in molecular knots.

In this note we generalize a result by Alekseev and Strobl for the case of $p$-branes. We show that there is a relation between anomalous free current algebras and "isotropic" involutive subbundles of $T\oplus \wedge^p T^*$ with the Vinogradov bracket, that is a generalization of the Courant bracket. As an application …

CT improves neural network performance on cell complex data.

In this paper, we give a new genus-3 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds. This formula also applies to intersection numbers on moduli spaces of spin curves. A by-product of the proof of this formula is a new relation in the tautological ring of the moduli space of…

Survey on manifold complexities and motion planning in robotics.

Extends topological groupoids and studies their properties.

Data science enhances knot theory by analyzing invariant relations.

Legendre transformations link related integrable hierarchies.

Homology and cohomology theory for topological quandles computed.

Study distance functions on manifolds linking geometry to topology.

We describe a topological field theory that studies the moduli space of solutions of the symplectic vortex equations. It contains as special cases the topological sigma-model and topological Yang-Mills over Kahler surfaces. The correlation functions of the theory are closely related to the recently introduced Hamiltoni…

Lectures on topological field theories and differential cohomology.

Novel TRI-GNN framework improves graph classification robustness.

To every oriented link $L$, we associate a topologically defined biquandle $\widehat{\mathcal{B}}_{L}$, which we call the topological biquandle of $L$. The construction of $\widehat{\mathcal{B}}_{L}$ is similar to the topological description of the fundamental quandle given by Matveev. We find a presentation of the top…

We give two applications of the 2-Engel relation, classically studied in finite and Lie groups, to the 4-dimensional topological surgery conjecture. The A-B slice problem, a reformulation of the surgery conjecture for free groups, is shown to admit a homotopy solution. We also exhibit a new collection of universal surg…

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.

A new deep learning framework for topological data.

We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.

The article applies Lusternik-Schnirelmann theory to establish lower bounds on critical points using sequential and parametrized topological complexity.

The Jacobi identity is the key relation in the definition of a Lie algebra. In the last decade, it also appeared at the heart of the theory of finite type invariants of knots, links and 3-manifolds (and is there called the IHX-relation). In addition, this relation was recently found to arise naturally in a theory of em…

We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a String structure and a Fivebrane structure, respectively. For the former, we study h…

Distance function to a finite set is a topological Morse function.

The paper explores gaps in curvature-related metrics and rigidity.

The study explores surfaces with curvature satisfying a specific relation, leading to isometric immersions and topological obstructions.

This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and there are nine chapters in total: 1. Combinatorial Complexes 2. Topological Invariants 3. Coverings 4. Galois Theory 5. G…

The paper proves finite topological type theorems for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume.

Analyzes string topology operations using Chen's integrals and homotopy transfer.

Clarifies definitions of global hyperbolicity in various spaces.

Surveying methods to create spaces with non-trivial self covers.

This paper formalizes the h-principle and sphere eversion in differential topology.

We relate the Andrews-Curtis conjecture to the triviality problem for balanced presentations of groups using algorithms from 3-manifold topology. Implementing this algorithm could lead to counterexamples to the Andrews-Curtis conjecture.

The paper generalizes relations between dynamical series and resolvents of vector fields.

Paper categorifies a polynomial related to ribbon graphs.

In this work, we formalize the problem of causal inference over graph-based relational time-series data where each node in the graph has one or more time-series associated to it. We propose causal inference models for this problem that leverage both the graph topology and time-series to accurately estimate local causal…

Find limiting sets for digital cones and suspensions.

Characterizes multitwists in surface mapping class groups.

A topological groupoid G is K-pointed, if it is equipped with a homomorphism from a topological group K to G. We describe the homotopy groups of such K-pointed topological groupoids and relate these groups to the ordinary homotopy groups in terms of a long exact sequence. As an application, we give an obstruction to pr…

Survey of Floer theories and their connections.

Globalizes Jones and Alexander polynomials using topological intersections.