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.
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.
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.
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…
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∞\(\tilde M^3 = 0\).
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.
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.
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.
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.
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.