For every finitely generated abelian group G, we construct an irreducible
open 3-manifold M[subscript G] whose end set is homeomorphic to a Cantor set and
whose homogeneity group is isomorphic to G. The end homogeneity group
is the group of self-homeomorphisms of the end set that extend to homeomorphisms
of...
For each Cantor set C in R³, all points of which have bounded local genus, we show that there are infinitely many inequivalent Cantor sets in R³ with the complement having the same fundamental group as the complement of C. This answers a question from Open Problems in Topology and...
We construct uncountably many simply connected open
3-manifolds with genus one ends homeomorphic to the Cantor set.
Each constructed manifold has the property that any self homeomorphism of the manifold (which necessarily extends to a homeomorphism of the ends) fixes the ends pointwise. These manifolds
are complements of rigid generalized...
We study a class M of cyclically presented groups that includes both finite and infinite groups and is defined by a certain combinatorial condition on the defining relations. This class includes many finite metacyclic generalized Fibonacci groups that have been previously identified in the literature. By analyzing their shift extensions...
Cellular sets in the Hilbert cube are the intersection of nested sequences of normal
cubes. One way of getting cellular maps on the Hilbert cube is by decomposing the Hilbert
cube into cellular sets and using a quotient map. By using a cellular decomposition of the
Hilbert cube, an example...
Let H be a cyclically-presented group on n generators with a single defining relator. Attempts have been made to classify such groups by their order, their status as a 3-manifold group, and the asphericity status of their presentations. For groups with a defining relator of length 3 these classifications are...
This thesis is devoted to determining structure results on a group relative to a subgroup, using information about the kernel of the boundary map of associated free resolutions. If Y is a CW-complex with homotopy type K(G,1) then for n ≥ 2 the nth skeletal homotopy module, hn(Y ) =...