Search results for "Geometry and Topology"

showing 10 items of 457 documents

Sigma-fragmentability and the property SLD in C(K) spaces

2009

Abstract We characterize two topological properties in Banach spaces of type C ( K ) , namely, being σ-fragmented by the norm metric and having a countable cover by sets of small local norm-diameter (briefly, the property norm-SLD). We apply our results to deduce that C p ( K ) is σ-fragmented by the norm metric when K belongs to a certain class of Rosenthal compacta as well as to characterize the property norm-SLD in C p ( K ) in case K is scattered.

CombinatoricsDiscrete mathematicsClass (set theory)Property (philosophy)Cover (topology)Metric (mathematics)Banach spaceSigmaCountable setGeometry and TopologyMathematicsTopology and its Applications
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Zur Hyperebenenalgebraisierung in desargues-Schen projektiven Verbandsgeometrien

1991

As a completion and extension of a result of A. Day and D. Pickering [5] we obtain the following structure theorem in the conceptual frame of projective lattice geometries: In a Desarguesian projective geometry the subgeometry of every at least one-dimensional hyperplane is module induced.

CombinatoricsDiscrete mathematicsProjective harmonic conjugateCollineationBlocking setDuality (projective geometry)Projective spaceGeometry and TopologyProjective planeNon-Desarguesian planeProjective geometryMathematicsJournal of Geometry
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A Group-theoretical Finiteness Theorem

2008

We start with the universal covering space $${\*M^n}$$ of a closed n-manifold and with a tree of fundamental domains which zips it $${T\longrightarrow\*M^n}$$ . Our result is that, between T and $${\* M^n}$$ , is an intermediary object, $${T\stackrel{p} {\longrightarrow} G \stackrel{F}{\longrightarrow} \*M^n}$$ , obtained by zipping, such that each fiber of p is finite and $${T\stackrel{p}{\longrightarrow}G\stackrel{F}{\longrightarrow} \*M^n}$$ admits a section.

CombinatoricsDiscrete mathematicsSection (fiber bundle)Tree (descriptive set theory)Differential geometryCovering spaceGroup (mathematics)Hyperbolic geometryGeometry and TopologyAlgebraic geometryPL-structureDeveloping mapsPartial sectionCayley 2-complexMathematics
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Elementarteiler von Inzidenzmatrizen symmetrischer Blockpläne

1986

By a study of the integral code generated by the rows of the incidence matrix and its extention the following results are obtained: Let d 1,...,d V(d 1|d 2,d 2|d 3...) be the elementary divisors of the incidence matrix of a symmetric (v,n+λ, λ) design. Then d v=(n+λ)n/g.c.d. (n, λ). Moreover, if p is a prime such that p|n, p∤λ and if x p denotes the p-part of x, then (d idv+2−i) p =n p for 2≤i≤v. For projective planes it can be shown that d 1=···=d 3n−2=1, hence $$d_{n^2 - 2n{\text{ }} + {\text{ }}5} {\text{ }} = \cdots = d_{n^2 + n} = n$$ and $$d_{n^2 - n{\text{ }} + {\text{ }}1} = (n + 1)n$$ . The paper also contains some results about elementary divisors of incidence matrices G satisfyin…

CombinatoricsElementary divisorsGeometry and TopologyAlgebraic geometryProjective planePrime (order theory)MathematicsIncidence (geometry)Geometriae Dedicata
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k-Weakly almost convex groups and ? 1 ? $$\tilde M^3 $$

1993

We extend Cannon's notion ofk-almost convex groups which requires that for two pointsx, y on then-sphere in the Cayley graph which can be joined by a pathl1 of length ≤k, there is a second pathl2 in then-ball, joiningx andy, of bounded length ≤N(k). Ourk-weakly almost convexity relaxes this condition by requiring only thatl1 ∝l2 bounds a disk of area ≤C1(k)n1 - e(k) +C2(k). IfM3 is a closed 3-manifold with 3-weakly almost convex fundamental group, then π1∞\(\tilde M^3 = 0\).

CombinatoricsFundamental groupCayley graphDifferential geometryHyperbolic geometryBounded functionRegular polygonGeometry and TopologyAlgebraic geometryConvexityMathematicsGeometriae Dedicata
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Characterization of chain geometries of finite dimension by their automorphism group

1990

A large class of chain geometries of finite dimension is characterized as strong chain spaces possessing a distinguished group of automorphisms fixing two distant points.

CombinatoricsInner automorphismChain (algebraic topology)HolomorphSymmetric groupSO(8)Alternating groupOuter automorphism groupGeometry and TopologyAutomorphismMathematicsGeometriae Dedicata
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A knot without tritangent planes

1991

We show, with computations aided by a computer, that the (3,2)-curve on some standard torus (which topologically is the trefoil knot) has no tritangent planes, thus answering in the negative a conjecture of M. H. Freedman.

CombinatoricsKnot complementKnot invariantSeifert surfaceQuantum invariantGeometry and TopologyTricolorabilityMathematics::Geometric TopologyTrefoil knotMathematicsKnot (mathematics)Pretzel linkGeometriae Dedicata
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A knot without triple bitangency

1997

It is proved that certain trefoil knot has not triple bitangency, answering thus in the negative a conjecture of S. Izumiya and W. L. Marar.

CombinatoricsKnot complementMathematics::Algebraic GeometryConjectureGeometry and TopologyMathematics::Geometric TopologyKnot (mathematics)Pretzel linkTrefoil knotMathematicsJournal of Geometry
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The conjugacy problem in subgroups of right-angled Artin groups

2009

We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups (i.e. fundamental groups of configuration spaces of points in graphs), many hyperbolic groups, and it coincides with the class of fundamental groups of ``special cube complexes'' studied independently by Haglund and Wise.

CombinatoricsMathematics::Group TheoryConjugacy problemBraid groupGeometry and TopologyNatural classGraphMathematicsJournal of Topology
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The case of equality in the dichotomy of Mohammadi–Oh

2019

If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the horospheric group $N$, the Burger-Roblin measure associated to $\Gamma$ on the quotient of the frame bundle is $U$-recurrent.

CombinatoricsMathematics::Group TheoryIntegerDiscrete groupGroup (mathematics)Astrophysics::High Energy Astrophysical PhenomenaApplied MathematicsErgodicityGeometry and TopologyMeasure (mathematics)Frame bundleQuotientMathematicsJournal of Fractal Geometry
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