14,615 research outputs found
Linear representations of regular rings and complemented modular lattices with involution
Faithful representations of regular -rings and modular complemented
lattices with involution within orthosymmetric sesquilinear spaces are studied
within the framework of Universal Algebra. In particular, the correspondence
between classes of spaces and classes of representables is analyzed; for a
class of spaces which is closed under ultraproducts and non-degenerate finite
dimensional subspaces, the latter are shown to be closed under complemented
[regular] subalgebras, homomorphic images, and ultraproducts and being
generated by those members which are associated with finite dimensional spaces.
Under natural restrictions, this is refined to a --correspondence between
the two types of classes
Configuration spaces of rings and wickets
The main result in this paper is that the space of all smooth links in
Euclidean 3-space isotopic to the trivial link of n components has the same
homotopy type as its finite-dimensional subspace consisting of configurations
of n unlinked Euclidean circles (the "rings" in the title). There is also an
analogous result for spaces of arcs in upper half-space, with circles replaced
by semicircles (the "wickets" in the title). A key part of the proofs is a
procedure for greatly reducing the complexity of tangled configurations of
rings and wickets. This leads to simple methods for computing presentations for
the fundamental groups of these spaces of rings and wickets as well as various
interesting subspaces. The wicket spaces are also shown to be K(G,1)'s.Comment: 28 pages. Some revisions in the expositio
- …