21 citations · 86 across the 22 of their papers we have counts for
6 papers · 1 filter
Tree-like is not a transitive relation on paths
Jeremy Brazas, Gregory R. Conner, Paul Fabel +1
The notions of tree-like loop and Lipschitz tree-like loop were introduced by Hambly and Lyons in their 2010 Annals of Mathematics paper. They showed that the Lipschitz tree-like p…
Thick Spanier groups and the first shape group
Jeremy Brazas, Paul Fabel
We develop a new route through which to explore , the kernel of the -shape group homomorphism determined by a general space , and establish, for each locally path…
The Hawaiian earring group and metrizability
Paul Fabel
Endowed with quotient topology inherited from the space of based loops, the fundamental group of the Hawaiian earring fails to be metrizable. The fundamental group of any space whi…
The mapping class group of a disk with infinitely many holes
Paul Fabel
A left orderable completely metrizable topological group is exhibited containing Artin's braid group on infinitely many strands. The group is the mapping class group (rel boundary)…
Isotopies of planar compacta need not extend to isotopies of planar continua
Paul Fabel
We construct an isotopy of a planar compactum that is not the restriction of an isotopy of any planar continuum.
Completing Artin's braid group on infinitely many strands
Paul Fabel
A generalization of the topological fundamental group is developed in order to exhibit a topologically complete braid group containing Artin's braid group on infinitely many strand…