DSpace Collection:
http://hdl.handle.net/10077/4160
Sun, 05 Feb 2023 14:59:09 GMT2023-02-05T14:59:09ZFinite Simple Groups Acting on 3-Manifolds and Homology Spheres
http://hdl.handle.net/10077/4252
Title: Finite Simple Groups Acting on 3-Manifolds and Homology Spheres
Authors: Reni, Marco; Zimmermann, Bruno
Abstract: Any fi{}nite group admits actions on closed 3-manifolds, and in particular
free actions. For actions with fi{}xed points, assumptions on the
type of the fi{}xed point sets of elements drastically reduce the
types of the possible groups. Concentrating on the basic case of fi{}nite
simple groups we show in the present paper that, if some involution
of a fi{}nite simple group G acting orientation-preservingly on a
closed orientable 3-manifold has nonempty connected fi{}xed point
set, then G is isomorphic to a projective linear group PSL(2, q),
and thus of a very restricted type. The question was motivated by
our work on the possible types of isometry groups of hyperbolic 3-manifolds
occuring as cyclic branched coverings of knots in the 3-sphere. We
characterize also fi{}nite groups which admit actions on $\mathbb{Z}_{2}$-homology
spheres, generalizing corresponding results for integer homology spheres.Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10077/42522001-01-01T00:00:00ZA Robust Algorithm to Determine the Topology of Space from the Cosmic Microwave Background Radiation
http://hdl.handle.net/10077/4251
Title: A Robust Algorithm to Determine the Topology of Space from the Cosmic Microwave Background Radiation
Authors: Weeks, Jeffrey R.
Abstract: Satellite measurements of the cosmic microwave back-ground radiation will soon provide an opportunity to test whether
the universe is multiply connected. This paper presents a new
algorithm for deducing the topology of the universe from the microwave background data. Unlike an older algorithm, the new
algorithm gives the curvature of space and the radius of the last
scattering surface as outputs, rather than requiring them as inputs. The new algorithm is also more tolerant of errors in the
observational data.Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10077/42512001-01-01T00:00:00ZHeegaard Reducing Spheres for the 3-Sphere
http://hdl.handle.net/10077/4250
Title: Heegaard Reducing Spheres for the 3-Sphere
Authors: Scharlemann, Martin
Abstract: There is a natural way of indexing the difference between
two collections of reducing spheres for the standard genus
g Heegard splitting of S3. Any two collections are related by a sequence
of collections, any two of which differ by low index, hence
in a simple way.Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10077/42502001-01-01T00:00:00ZSurgery description of orientation-preserving periodic maps on compact orientable 3-manifolds
http://hdl.handle.net/10077/4249
Title: Surgery description of orientation-preserving periodic maps on compact orientable 3-manifolds
Authors: Sakuma, Makoto
Abstract: We show that every orientation-preserving periodic diffeomorphism
f on a closed orientable 3-manifold M has a \textquotedblleft{}surgery
description\textquotedblright{}, that is, there is a framed link $\mathcal{L}\;\textrm{in}\; S^{3}$
which is invariant by a standard rotation $\varphi$ around a trivial
knot, such that M is obtained by surgery on $\varphi$ and that f
is conjugate to the periodic diff{}eomorphism induced by $\varphi$.
We will illustrate this result, by visualizing isometries of the complements
of 2-component hyperbolic links with $\leq$ 9 crossings which do
not extend to periodic maps of $S^{3}$.Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10077/42492001-01-01T00:00:00Z