arXiv research

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

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

New stability theorem for nonorientable surfaces mapping class groups.

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

Maximal dilatation found on nonorientable surfaces.

Generators found for nonorientable surfaces with many punctures.

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

This paper extends quasimorphism results to nonorientable surfaces.

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

Two elements generate all mappings of a nonorientable surface.

Minimal involutions generate a subgroup of nonorientable surfaces.

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

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.

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

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

New findings on generating mapping class groups of nonorientable surfaces.

Minimal singular fibers found in nonorientable Lefschetz fibrations.

Uniform hyperbolicity proved for nonorientable surface curve graphs.

Automorphism group of nonorientable surface curve graph matches surface homeomorphisms.

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 …

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…

Geography problem for nonorientable surfaces bounded by knots.

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.

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

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

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 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.

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

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…

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).

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.

Classifies homomorphisms from braid groups to mapping class groups of nonorientable surfaces.

Survey of minimal generating sets for nonorientable mapping class groups.

We classify incompressible, boundary-incompressible, nonorientable surfaces in punctured-torus bundles over $S^1$. We use the ideas of Floyd, Hatcher, and Thurston. The main tool is to put our surface in the "Morse position" with respect to the projection of the bundle into the basis S^1.

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

We prove that each injective simplicial map from the arc complex of a compact, connected, nonorientable surface with nonempty boundary to itself is induced by a homeomorphism of the surface. We also prove that the automorphism group of the arc complex is isomorphic to the quotient of the mapping class group of the surf…

The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space are studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence, some existence and uniqueness results for maximal Moebius strips and maximal Klei…

We show that any pseudo-Anosov map that is a lift of pseudo-Anosov homeomorphism of a nonorientable surface has vanishing SAF invariant. We also provide a criterion to certify that a pseudo-Anosov map is not such a lift.

We obtain a simple presentation of the hyperelliptic mapping class group $M^h(N)$ of a nonorientable surface N. As an application we compute the first homology group of $M^h(N)$ with coefficients in $H_1(N;Z)$.

Given an embedded cylinder in an arbitrary surface, we give a gauge theoretic definition of the associated Goldman flow, which is a circle action on a dense open subset of the moduli space of equivalence classes of flat SU(2)-connections over the surface. A cylinder in a compact nonorientable surface lifts to two cylin…

We obtain a finite set of generators for the level 2 mapping class group of a closed nonorientable surface of genus $g\ge 3$. This set consists of isotopy classes of Lickorish's Y-homeomorphisms also called crosscap slides.

We determine the smallest stretch factor among pseudo-Anosov maps with an orientable invariant foliation on the closed nonorientable surfaces of genus 4, 5, 6, 7, 8, 10, 12, 14, 16, 18 and 20. We also determine the smallest stretch factor of an orientation-reversing pseudo-Anosov map with orientable invariant foliation…

We prove that the hyperelliptic mapping class group of a nonorientable surface of genus $g\geq 4$ has a faithful linear representation of dimension $g^2-1$ over $\mathbb{R}$.

We prove that each superinjective simplicial map of the complex of curves of a compact, connected, nonorientable surface is induced by a homeomorphism of the surface, if $(g, n) \in \{(1, 0), (1, 1), (2, 0), (2, 1), (3, 0)\}$ or $g + n \geq 5$, where $g$ is the genus of the surface and $n$ is the number of the boundary…

Crosscap slide is a homeomorphism of a nonorientable surface of genus at least 2, which was introduced under the name Y-homeomorphism by Lickorish as an example of an element of the mapping class group which cannot be expressed as a product of Dehn twists. We prove that the subgroup of the mapping class group of a clos…

Let $N_{g,n}$ denote the nonorientable surface of genus $g$ with $n$ boundary components and $M(N_{g,n})$ its mapping class group. We obtain an explicit finite presentation of $M(N_{g,n})$ for $n=0,1$ and all $g$ such that $g+n>3$.