Mapping arcwise connected continua onto cyclic continua
Mapping spaces and M-CW complexes.
Mappings Into Loop Spaces and Central Group Extensions.
Maps and Equivalences into Equalizing Fibrations and from Coequalizing Cofibrations.
Measurable cardinals and fundamental groups of compact spaces
We prove that all groups can be realized as fundamental groups of compact spaces if and only if no measurable cardinals exist. If the cardinality of a group G is nonmeasurable then the compact space K such that G = π₁K may be chosen so that it is path connected.
Miller spaces and spherical resolvability of finite complexes
Let 𝒜 be a fixed collection of spaces, and suppose K is a nilpotent space that can be built from spaces in 𝒜 by a succession of cofiber sequences. We show that, under mild conditions on the collection 𝒜, it is possible to construct K from spaces in 𝒜 using, instead, homotopy (inverse) limits and extensions by fibrations. One consequence is that if K is a nilpotent finite complex, then ΩK can be built from finite wedges of spheres using homotopy limits and extensions by fibrations. This is applied...
Minimal models for non-nilpotent spaces.
Mod p Decompositions of co-H-Spaces and Applications.
Modular Representations of GL (n, p), Splitting ...(...P...x...x---P...), and the ß-family as Framed Hypersurfaces.
Moduli spaces of covers and the Hurwitz monodromy group.
Multiple Points of Immersions, and the Kahn-Priddy Theorem.
Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)
The natural quotient map q from the space of based loops in the Hawaiian earring onto the fundamental group provides a naturally occuring example of a quotient map such that q × q fails to be a quotient map. With the quotient topology, this example shows π₁(X,p) can fail to be a topological group if X is locally path connected.