scholarly journals A diagrammatic presentation and its characterization of non-split compact surfaces in the 3-sphere

2021 ◽  
Author(s):  
Shosaku Matsuzaki
Keyword(s):  
Compact Surface ◽  
Reidemeister Moves ◽  
Trivalent Graphs ◽  
Embedded Surfaces ◽  
Compact Surfaces

We give a presentation for a non-split compact surface embedded in the 3-sphere [Formula: see text] by using diagrams of spatial trivalent graphs equipped with signs and we define Reidemeister moves for such signed diagrams. We show that two diagrams of embedded surfaces are related by Reidemeister moves if and only if the surfaces represented by the diagrams are ambient isotopic in [Formula: see text].

SELF-INTERSECTION NUMBERS OF PATHS IN COMPACT SURFACES

2011 ◽  
Vol 20 (03) ◽  
pp. 403-410 ◽  
Author(s):  
LORENA ARMAS-SANABRIA ◽  
FRANCISCO GONZÁLEZ-ACUÑA ◽  
JESÚS RODRÍGUEZ-VIORATO
Keyword(s):  
Free Group ◽  
Intersection Number ◽  
Compact Surface ◽  
Simple Path ◽  
Intersection Numbers ◽  
Minimal Self ◽  
Compact Surfaces

In this paper, we give an algorithm to calculate the minimal self-intersection number of paths in a compact surface with boundary representing a given element of the free group F(x1, x2, …, xn). In particular, this algorithm says whether or not a word in x1, x2, …, xn is representable by a simple path. Our algorithm is simpler than similar algorithms given previously. In the case of a disk with n holes the problem is equivalent to the problem of deciding which relators can appear in an Artin n-presentation.

scholarly journals THE ENERGY-MOMENTUM TENSOR ON LOW DIMENSIONAL Spinc MANIFOLDS

2012 ◽  
Vol 23 (09) ◽  
pp. 1250090 ◽  
Author(s):  
GEORGES HABIB ◽  
ROGER NAKAD
Keyword(s):  
Energy Momentum Tensor ◽  
Type Inequality ◽  
Momentum Tensor ◽  
Compact Surface ◽  
Round Sphere ◽  
Spinor Equation ◽  
Immersed Surfaces ◽  
Low Dimensional ◽  
Limiting Case

On a compact surface endowed with any Spinc structure, we give a formula involving the Energy-Momentum tensor in terms of geometric quantities. A new proof of a Bär-type inequality for the eigenvalues of the Dirac operator is given. The round sphere 𝕊2 with its canonical Spinc structure satisfies the limiting case. Finally, we give a spinorial characterization of immersed surfaces in 𝕊2 × ℝ by solutions of the generalized Killing spinor equation associated with the induced Spinc structure on 𝕊2 × ℝ.

scholarly journals Transitivity of surface dynamics lifted to Abelian covers

2009 ◽  
Vol 29 (5) ◽  
pp. 1417-1449 ◽  
Author(s):  
PHILIP BOYLAND
Keyword(s):  
Finite Type ◽  
Spectral Radius ◽  
Compact Surface ◽  
Surface Dynamics ◽  
Subshift Of Finite Type ◽  
Abelian Cover ◽  
Abelian Covers

AbstractA homeomorphismfof a manifoldMis calledH1-transitive if there is a transitive lift of an iterate offto the universal Abelian cover$\tilde {M}$. Roughly speaking, this means thatfhas orbits which repeatedly and densely explore all elements ofH1(M). For a rel pseudo-Anosov map ϕ of a compact surfaceMwe show that the following are equivalent: (a) ϕ isH1-transitive, (b) the action of ϕ onH1(M) has spectral radius one and (c) the lifts of the invariant foliations of ϕ to$\tilde {M}$have dense leaves. The proof relies on a characterization of transitivity for twisted ℤd-extensions of a transitive subshift of finite type.

scholarly journals Fixed subgroups are compressed in surface groups

2015 ◽  
Vol 25 (05) ◽  
pp. 865-887 ◽  
Author(s):  
Qiang Zhang ◽  
Enric Ventura ◽  
Jianchun Wu
Keyword(s):  
Positive Solution ◽  
Compact Surface ◽  
Surface Groups ◽  
Direct Products ◽  
Fixed Subgroups ◽  
The Way

For a compact surface Σ (orientable or not, and with boundary or not), we show that the fixed subgroup, Fix ℬ, of any family ℬ of endomorphisms of π1(Σ) is compressed in π1(Σ), i.e. rk ( Fix ℬ) ≤ rk (H) for any subgroup Fix ℬ ≤ H ≤ π1(Σ). On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, G, of finitely many free and surface groups, and give a characterization of when G satisfies that rk ( Fix ϕ) ≤ rk (G) for every ϕ ∈ Aut (G).

scholarly journals A Note on a Multiplicity Result for the Mean Field Equation on Compact Surfaces

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Aleks Jevnikar
Keyword(s):  
Field Equation ◽  
Mean Field ◽  
Compact Surface ◽  
Multiplicity Result ◽  
The Mean ◽  
Compact Surfaces ◽  
Mean Field Equation

AbstractWe are concerned with the class of equations with exponential nonlinearitieson a compact surface Σ, which describes the mean field equation of equilibrium turbulence with arbitrarily signed vortices. Here,

scholarly journals Performance of a formaldehyde-free sesame protein adhesive modified by urea in the presence and absence of glyoxal

BioResources ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. 3121-3136
Author(s):  
Xiaobo Wei ◽  
Yuxiang Ma ◽  
Xuede Wang
Keyword(s):  
Water Resistance ◽  
Formaldehyde Emission ◽  
Wood Adhesive ◽  
Sesame Oil ◽  
Compact Surface ◽  
Process Industry ◽  
Type Ii ◽  
High Quality Protein ◽  
Sesame Cake

Sesame cake and meal, byproducts of the sesame oil process industry and mainly used as feed and fertilizer, are often not optimally utilized and are wasted when the material could be used as a high-quality protein source. This research primarily emphasizes the preparation of a sesame protein-based adhesive with urea and glyoxal modification to use as a wood adhesive. The performance and characterization of the urea and glyoxal modified sesame protein adhesive (USP and GUSP, respectively) were measured precisely. After glyoxal was added, the water resistance of the GUSP adhesive was significantly enhanced, reaching the standard for Type II plywood. The formaldehyde emission test showed that the GUSP adhesive could be utilized as a formaldehyde-free wood adhesive, having a significantly lower than the demand of the E0 level (i.e., 0.5 mg/L). Furthermore, increasing the glyoxal content in the adhesives enhanced the thermal stability but not significantly. A substance with a crosslinking structure was formed from the reaction between the sesame protein and glyoxal, which enhanced the water resistance. Meanwhile, the fractured structure of the GUSP adhesive having a compact surface also was propitious to enhance the water resistance. Thus, the GUSP adhesive could be used as a novel adhesive in plywood fabrication.

scholarly journals Semi-rigidity of horocycle flows over compact surfaces of variable negative curvature

1987 ◽  
Vol 7 (1) ◽  
pp. 49-72 ◽  
Author(s):  
J. Feldman ◽  
D. Ornstein
Keyword(s):  
Invariant Measure ◽  
Tangent Bundle ◽  
Geodesic Flow ◽  
Negative Curvature ◽  
Compact Surface ◽  
Maximal Entropy ◽  
Unit Tangent Bundle ◽  
Compact Surfaces ◽  
Measure Of Maximal Entropy

AbstractLet g be the geodesic flow on the unit tangent bundle of a C3 compact surface of negative curvature. Let μ be the g-invariant measure of maximal entropy. Let h be a uniformly parametrized flow along the horocycle foliation, i.e., such a flow exists, leaves μ invariant, and is unique up to constant scaling of the parameter (Margulis). We show that any measure-theoretic conjugacy: (h, μ) → (h′, μ′) is a.e. of the form θ, where θ is a homeomorphic conjugacy: g → g′. Furthermore, any homeomorphic conjugacy g → g′; must be a C1 diffeomorphism.

scholarly journals Four-dimensional aspects of tight contact 3-manifolds

2021 ◽  
Vol 118 (22) ◽  
pp. e2025436118
Author(s):  
Matthew Hedden ◽  
Katherine Raoux
Keyword(s):  
Euler Characteristic ◽  
Contact Structure ◽  
Fiber Surface ◽  
Affirmative Answer ◽  
Contact Structures ◽  
Torus Knots ◽  
Tight Contact ◽  
Embedded Surfaces ◽  
Fibered Link

We conjecture a four-dimensional characterization of tightness: A contact structure on a 3-manifold Y is tight if and only if a slice-Bennequin inequality holds for smoothly embedded surfaces in Y×[0,1]. An affirmative answer to our conjecture would imply an analogue of the Milnor conjecture for torus knots: If a fibered link L induces a tight contact structure on Y, then its fiber surface maximizes the Euler characteristic among all surfaces in Y×[0,1] with boundary L. We provide evidence for both conjectures by proving them for contact structures with nonvanishing Ozsváth–Szabó contact invariant.

scholarly journals Linearization of topologically Anosov homeomorphisms of non compact surfaces of genus zero and finite type

2021 ◽  
pp. 1-11
Author(s):  
Gonzalo Cousillas ◽  
Jorge Groisman ◽  
Juliana Xavier
Keyword(s):  
Finite Type ◽  
Compact Surface ◽  
Genus Zero ◽  
Compact Surfaces

We study the dynamics of {\it topologically Anosov} homeomorphisms of non-compact surfaces. In the case of surfaces of genus zero and finite type, we classify them. We prove that if $f\colon S \to S$, is a Topologically Anosov homeomorphism where $S$ is a non-compact surface of genus zero and finite type, then $S= \mathbb{R}^2$ and $f$ is conjugate to a homothety or reverse homothety (depending on wether $f$ preserves or reverses orientation). A weaker version of this result was conjectured in \cite{cgx}.

Sign in / Sign up

Export Citation Format

Share Document