arXiv research

Nonorientable 4-manifolds can be fibred over 2-disks with nonorientable fibers.

Study of alternating links on nonorientable surfaces, extending results to nonorientable projections.

The study explores nonorientable 3-manifolds using open books and their monodromies.

We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid non-bipartite crystallizations up to 30 vertices.

Study on embedding surfaces into 3-manifolds, focusing on equivariant cases.

We consider finite group-actions on closed, orientable and nonorientable 3-manifolds; such a finite group-action leaves invariant the two handlebodies of a Heegaard splitting of M of some genus g. The maximal possible order of a finite group-action of an orientable or nonorientable handlebody of genus g > 1 is 24(g-1),…

Paper classifies link diagrams on nonorientable surfaces using region crossing changes.

New method shows nonorientable surfaces in 4D are topologically unknotted.

New stability theorem for nonorientable surfaces mapping class groups.

Study on nonorientable 4-manifolds using simplified fibrations and trisections.

Study shows pants graph automorphisms match mapping class groups of nonorientable surfaces.

Minimal singular fibers found in nonorientable Lefschetz fibrations.

Maximal dilatation found on nonorientable surfaces.

We construct complete nonorientable minimal surfaces whose Gauss map omits two points of the projective plane. This result proves that Fujimoto's theorem is sharp in nonorientable case.

Generators found for nonorientable surfaces with many punctures.

The study explores large group actions on 3-manifolds and their Heegaard splittings.

Two elements generate all mappings of a nonorientable surface.

Minimal involutions generate a subgroup of nonorientable surfaces.

This paper extends quasimorphism results to nonorientable surfaces.

Starting with an ideal triangulation of the interior of a compact 3-manifold M with boundary, no component of which is a 2-sphere, we provide a construction, called an inflation of the ideal triangulation, to obtain a strongly related triangulations of M itself. Besides a step-by-step algorithm for such a construction,…

Zeta functions extended to nonorientable surfaces, order of vanishing computed.

Optimal inequalities for systole, inradius, and volume in hyperbolic 3-manifolds

Geography problem for nonorientable surfaces bounded by knots.

New findings on generating mapping class groups of nonorientable surfaces.

New bounds on nonorientable four-ball genus for torus knots.

The nonorientable four-ball genus of a knot K is the smallest first Betti number of any smoothly embedded, nonorientable surface F in B^4 bounding K. In contrast to the orientable four-ball genus, which is bounded below by the Murasugi signature, the Ozsvath-Szabo tau-invariant, the Rasmussen s-invariant, the best lowe…

Nonorientable spanning surfaces of periodic knots can have arbitrarily high first Betti number.

Study on maximal surfaces with high genus in Lorentz-Minkowski space.

The paper shows how to unknot certain nonorientable surfaces in 4-dimensional spaces.

In arXiv:math/0605587, the first two authors have constructed a gauge-equivariant Morse stratification on the space of connections on a principal U(n)-bundle over a connected, closed, nonorientable surface. This space can be identified with the real locus of the space of connections on the pullback of this bundle over …

New classification of nonorientable 4-manifolds with specific fundamental groups.

Study on nonorientable 4-genus of double twist knots.

Uniform hyperbolicity proved for nonorientable surface curve graphs.

On each nonorientable surface of odd genus $g \geq 5$, we give a mapping class whose dilatation on an invariant subsurface is the golden ratio.

We prove that any minimal weak symplectic filling of the canonical contact structure on the unit cotangent bundle of a nonorientable closed surface other than the real projective plane is s-cobordant rel boundary to the disk cotangent bundle of the surface. If the nonorientable surface is the Klein bottle, then we show…

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

The nonorientable 4-genus $γ_4(K)$ of a knot $K$ is the smallest first Betti number of any nonorientable surface properly embedded in the 4-ball, and bounding the knot $K$. We study a conjecture proposed by Batson about the value of $γ_4$ for torus knots, which can be seen as a nonorientable analogue of Milnor's Conjec…

Automorphism group of nonorientable surface curve graph matches surface homeomorphisms.

The study bounds the excess of disjoint nonorientable surfaces in a 4-manifold.

We obtain simple generating sets for various mapping class groups of a nonorientable surface with punctures and/or boundary. We also compute the abelianizations of these mapping class groups.

Proves mapping class group of nonorientable surfaces can be generated by three torsions.

Let t_a be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, I(t_a^n(b),b)=|n|I(a,b)^2, where I(,) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties o…

We determine the first homology group of the mapping class group M(N) of a nonorientable surface N with coefficients in H_1(N;Z).

Survey of minimal generating sets for nonorientable mapping class groups.

We show that Norbury's McShane identity for nonorientable cusped hyperbolic surfaces N generalizes to quasifuchsian representations of pi_1(N) as well as pseudo-Anosov mapping Klein bottles with singular fibers given by N.

Klein bottle embeds into specific lens spaces.

A crosscap transposition is an element of the mapping class group of a nonorientable surface represented by a homeomorphism supported on a one-holed Klein bottle and swapping two crosscaps. We prove that the mapping class group of a compact nonorientable surface of genus $g\ge 7$ is generated by conjugates of one cross…

Embedding right-angled Artin groups in mapping class groups of nonorientable surfaces.