A homotopy double groupoid of a Hausdorff space.
A homotopy double groupoid of a Hausdorff space. II: A van Kampen theorem.
Compositions of equi-dimensional fold maps
According to Ando's theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket in the stable stem through Ando's isomorphism. By using these operations we explicitly construct several fold maps with convenient properties, including a fold map which represents the generator of the stable 6-stem.
Framing Sphere Bundles over Spheres, the Smith Pairing, and Three-Fold Toda Brackets.
Groupoids, stability cokernel sequences and duality
Higher homotopy groupoids and Toda brackets.
Loop spaces and homotopy operations
We describe an obstruction theory for an H-space X to be a loop space, in terms of higher homotopy operations taking values in . These depend on first algebraically “delooping” the Π-algebras , using the H-space structure on X, and then trying to realize the delooped Π-algebra.
Zur Struktur der Puppe-Folge für halbexakte Funktoren.