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Nonlocal loss of first homotopy in polyhedral approximations of Peano continua
Jeremy Brazas, Hanspeter Fischer
If a Peano continuum is semilocally simply connected, then it has a finite polyhedral approximation whose fundamental group is isomorphic to that of . In general, this fails…
Higher homotopy wild sets
Jeremy Brazas, Atish Mitra
The -wild set of a topological space is the subspace of consisting of the points at which there exists a shrinking sequence of essential based maps…
The Čech homotopy groups of a shrinking wedge of spheres
Jeremy Brazas
We compute the Čech homotopy groups of the -dimensional infinite earring space , i.e. a shrinking wedge of -spheres. In particular, for all , we prov…
Homotopy groups of shrinking wedges of non-simply connected CW-complexes
Jeremy Brazas
In this paper, we study the homotopy groups of a shrinking wedge of a sequence of non-simply connected CW-complexes. Using a combination of generalized covering space…
Sequential -connectedness and infinite factorization in higher homotopy groups
Jeremy Brazas
A space is "sequentially -connected" at if for every and sequence of maps that converges toward a point , the m…
The infinitary n-cube shuffle
Jeremy Brazas
In this paper, we formalize the sense in which higher homotopy groups are "infinitely commutative." In particular, we both simplify and extend the highly technical procedure, due t…