arXiv research

Hensel-Przytycki-Webb proved that all curve graphs of orientable surfaces are 17-hyperbolic. In this paper, we show that curve graphs of non-orientable surfaces are 17-hyperbolic by applying Hensel-Przytycki-Webb's argument. We also show that arc graphs of non-orientable surfaces are 7-hyperbolic, and arc-curve graphs …

Polynomial-time algorithm finds short non-orientable loops intersecting graph edges up to 30 times.

For graphs with 13 or more vertices, either the graph or its complement is intrinsically linked.

The pants graph of a non-orientable surface is quasi-isometric to its Teichmüller space.

Counting lattice points in moduli space of Klein surfaces.

The study examines flip-graphs of non-orientable surfaces and their diameters.

Study calculates integral cohomology of non-orientable infinite type surfaces.

Researchers prove any graph can be realized as Reeb graph, linking it to manifold properties.

This paper exhausts curve complexes on non-orientable surfaces.

Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P^2-irreducible 3-manifold triangulations. In particular, new constraints are proven for face pairing graphs, and pruning techniques are improved using a modification of the union-find alg…

The main result of this paper is a Pfaffian formula for the partition function of the dimer model on a graph G embedded in a closed, possibly non-orientable surface S. This formula is suitable for computational purposes, and it is obtained using purely geometrical methods. The key step in the proof consists of a corres…

The paper extends previous work on Reeb graphs of smooth functions on 3D manifolds to non-orientable cases.

The paper extends trisection theory to non-orientable 4-manifolds using colored triangulations.

Researchers found all embeddings of Kuratowski graphs on a double torus.

We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting thr…

Study trisections of non-orientable 4-manifolds with boundary.

The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible triangulation. In addition we present constraints upon the co…

This paper calculates the non-orientable 4-genus for knots with 10 crossings.

Study curves in non-orientable surfaces with specific intersection properties.

Analog of Kauffman bracket for non-orientable knots in thickened surface.

New method finds non-orientable knotted surfaces in 4D.

Researchers refine the non-orientable $4$-genus of torus knots using Batson's surfaces.

Minimal stretch factor for non-orientable surfaces is small.

The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in $\mathbb{R}^n$ for any $n\ge 3$. These methods, which we develop essentially from the first principles, enable us to prove that the space of conformal minimal immer…

Researchers compute bounds and formulas for non-orientable 4-genus of torus knots.

Presentations for involutions on non-orientable surfaces up to genus 5.

Simplified presentations for non-orientable surface mapping class groups.

Paper proves achiral Lefschetz fibrations from non-orientable Lefschetz fibrations.

New invariant distinguishes non-orientable surfaces.

Study on non-orientable surfaces for maximal disc packings.

Study on loops on non-orientable surfaces, determining cardinality and order.

We prove a version of the classical Runge and Mergelyan uniform approximation theorems for non-orientable minimal surfaces in Euclidean 3-space R3. Then, we obtain some geometric applications. Among them, we emphasize the following ones: 1. A Gunning-Narasimhan type theorem for non-orientable conformal surfaces. 2. An …

Study homology groups for non-orientable surfaces with boundary.

Study non-orientable 4-genus for 11-crossing non-alternating knots.

Study shows non-equivariant and equivariant non-orientable 4-genus of periodic knots can differ.

Classifies 3-manifolds from cube identifications.

This paper provides an infinite presentation for a subgroup of mapping class groups of non-orientable surfaces.

A spine is constructed for a non-orientable surface's decorated Teichmüller space.

Study on dimensions of mapping class groups of non-orientable surfaces.

We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct generalization of the one given in the eighties by S. Lins for closed 3-manifolds, which …

Corrects classification of Seifert fibrations for lens spaces with non-orientable bases.

Study on Legendrian knots and their non-orientable Lagrangian fillings.

Considering a solid 3-dimensional Klein bottle and a collaring of its boundary, can we extend a generic $C^\infty$ non-singular function defined on the collaring to the full solid Klein bottle without critical points? We give a condition on the Reeb graph of the given function that is necessary and sufficient for the e…

Study shows infinite-dimensional third bounded cohomology for non-orientable surfaces.

We show that the Lusternik-Schnirelmann category of the homotopy cofiber of the diagonal map for non-orientable surfaces equals three. Also, we prove that the topological complexity of non-orientable surfaces of genus $>3$ is four.

The free factor graph for Aut(F_N) is not hyperbolic.

The non-orientable 4-genus of a knot in the 3-sphere is defined as the smallest first Betti number of any non-orientable surface smoothly and properly embedded in the 4-ball, with boundary the given knot. We compute the non-orientable 4-genus for all knots with crossing number 8 or 9. As applications we prove a conject…

Study on non-orientable surfaces and inscribed rectangles in 4-manifolds.