0000000000068973
AUTHOR
C. Tanasi
showing 2 related works from this author
Equivariant, Almost-Arborescent Representations of Open simply-Connected 3-Manifolds; A Finiteness result
2004
When one extends the (almost) collapsible pseudo-spine representation theorem for homotopy 3-spheres [Po3] to open simply connected 3-manifolds V 3,new phenomena appear: at the source of the representation, the set of double points is, generally speaking, no longer closed. We show that at the cost of replacing V3 by Vh3 = {V3 with very many holes }, we can always find representations X2 →f V3 with X2 locally finite and almost-arborescent, with Ψ (f) = Φ(f), with the open regular neighbourhood (the only one which is well-defined here) Nbd(f X2) = Vh3 and such that on any precompact tight transversal to the set of double lines, we have only FINITELY many limit points (of the set of double poi…
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∞\(\tilde M^3 = 0\).