12 citations · 20 across the 5 of their papers we have counts for
6 papers
Explicit Acyclic Models and (Co)Chain Operations
Greg Brumfiel, John Morgan
We exploit a uniform recursive procedure to construct morphisms of chain complexes in a wide variety of situations, using free bases of domains and preferred null homotopies of…
A Cochain Level Proof of Adem Relations in the Mod 2 Steenrod Algebra
Greg Brumfiel, Anibal M. Medina-Mardones, John Morgan
In 1947, N.E. Steenrod defined the Steenrod Squares, which are mod 2 cohomology operations, using explicit cochain formulae for cup-i products of cocycles. He later recast the cons…
Quadratic Functions of Cocycles and Pin Structures
Greg Brumfiel, John Morgan
We construct a natural bijective correspondence between equivalence classes of Pin structures on a compact simplicial -manifold , possibly with boundary, and $\mathbb{Z…
The Pontrjagin Dual of 4-Dimensional Spin Bordism
Greg Brumfiel, John Morgan
The goal of this paper is to study the Pontrjagin dual of (reduced) 4-dimensional Spin bordism. That is to say, we consider the functor from the category of topological spaces to t…
The Pontrjagin Dual of 3-Dimensional Spin Bordism
Greg Brumfiel, John Morgan
For each space X we define an explicit group, G(X), functorially in X. This group is constructed from the groups of cochains on X. Furthermore, we construct an explicit functorial…
On finite index subgroups of a universal group
G. Brumfiel, H. Hilden, M. T. Lozano +5
The orbifold group of the Borromean rings with singular angle 90 degrees, , is a universal group, because every closed oriented 3--manifold occurs as a quotient space $M…