The topological fundamental group and hoop earring spaces
by
Jeremy Brazas
University of New Hampshire

The topological fundamental group has been used to generalize the classification theorem of covering spaces to spaces lacking universal covers and the resulting functor, p₁^top, assigning to each space a quasi-topological group, has been shown to be a finer invariant than the mere fundamental group. I will describe the topological fundamental group of the hoop earring space wS(X₊) of an arbitrary space X (the reduced suspension of X₊=X\sqcup {*} with a weak topology) and discuss how these computations may be useful in addressing some open problems such as the essential surjectivity of p₁^top and the classification of spaces whose topological fundamental group is a topological group.

Date received: November 24, 2009