Über das Geschlecht von Knoten
In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces...
On montre un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert. Plus précisément, en toute dimension , il existe une constante telle que, pour tout ouvert proprement convexe , pour tout point , tout groupe discret engendré par un nombre fini d’automorphismes de qui déplacent le point de moins de est virtuellement nilpotent.
There is a disk in S3 whose interior is PL embedded and whose boundary has a tame Cantor set of locally wild points, such that the n-fold cyclic coverings of S3 branched over the boundary of the disk are all S3. An uncountable set of inequivalent wild knots with these properties is exhibited.
Nous donnons une nouvelle construction cohomologique du cœur de l'invariant de Casson et nous donnons un nouveau calcul de ses valeurs sur les générateurs du sous- groupe de Johnson du mapping class group.
For every rational homology 3-sphere with H₁(M,ℤ) = (ℤ/2ℤ)ⁿ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root, and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of...