On -equivariant homology.
In the study of surfaces in 3-manifolds, the so-called ?cut-and-paste? of surfaces is frequently used. In this paper, we generalize this method, in a sense, to singular-surfaces, and as an application, we prove that two collections of singular-disks in the 3-space R3 which span the same trivial link are link-homotopic in the upper-half 4-space R3 [0,8) keeping the link fixed. Throughout the paper, we work in the piecewise linear category, consisting of simplicial complexes and piecewise linear maps....
Related to Shape Theory, in a previous paper (1992) we studied weak monomorphisms and weak epimorphisms in the category of pro-groups. In this note we give some intrinsic characterizations of the weak monomorphisms and the weak epimorphisms in pro-HTop* in the case when one of the two objects of such a morphism is a rudimentary system.
[For the entire collection see Zbl 0699.00032.] A connection structure (M,H) and a path structure (M,S) on the manifold M are called compatible, if locally where and express the semi-spray S and the connection map H, resp. In the linear case of H its geodesic spray S is quadratic: On the contrary, the homogeneity condition of S induces the relation for the compatible connection H, whence it follows not that H is linear, i.e. if a connection structure is compatible with a spray, then...