This paper uses Brin and Thickstun’s theory of end reductions of noncompact 3-manifolds to study groups of covering translations of irreducible contractible open 3-manifolds W which are not homeomorphic to R. We associate to W an object S(W ) called the simplicial complex of minimal R-irreducible end reductions of W . Whenever W covers another 3-manifold the group of covering translations is is...

We prove that for any superatomic Boolean Algebra of cardinality > i4 there is an automorphism moving uncountably many atoms. Similarly for larger cardinals. Any of those results are essentially best possible

We present two short proofs for Diestel's criterion that a connected graph has normal spanning tree provided it contains no subdivision of countable clique in which every edge been replaced by uncountably many parallel edges.

We introduce a variant of the canonical base property, called transfer internality to quotients. A structural study groups definable in theories with this property yields as consequence infinitely many new uncountably categorical additive covers o

An uncountable collection of arcs in S is constructed, each member of which is wild precisely at its endpoints, such that the fundamental groups of their complements are non-trivial, pairwise non-isomorphic, and indecomposable with respect to free products. The fundamental group of the complement of a certain Fox-Artin arc is also shown to be indecomposable.

We introduce and study the notion of a chain group of homeomorphisms of a one-manifold, which is a certain generalization of Thompson’s group F. Precisely, this is a group finitely generated by homeomorphisms, each supported on exactly one interval in a chain, and subject to a certain mild dynamical condition. The resulting class of groups exhibits a combination of uniformity and diversity. On ...

In this paper we consider a free associative algebra on three generators over an arbitrary field K. Given a term ordering on the commutative polynomial ring on three variables over K, we construct uncountably many liftings of this term ordering to a monomial ordering on the free associative algebra. These monomial orderings are total well orderings on the set of monomials, resulting in a set of...

It is shown that all but at most countably many spaces in the genus of HP∞, the infinite quaternionic projective space, do not admit any essential maps from CP∞, the infinite complex projective space. This strengthens a theorem of McGibbon and Rector which states that among the uncountably many homotopy types in its genus, HP∞ is the only one which admits a maximal torus.

Answering a question raised by Glasner and Rudolph (1984) we construct uncountably many strictly ergodic topological systems which are metrically isomorphic to a given ergodic system (X,63, #, T) but not almost topologically conjugate to it.

It is well known that the time average or the center of mass for generic orbits of the standard tent map is 0.5. In this paper we show some interesting properties of the exceptional orbits, including periodic orbits, orbits without mass center, and orbits with mass centers different from 0.5. We prove that for any positive integer n, there exist n distinct periodic orbits for the standard tent ...