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On shape

Ralph Fox (1972)

Fundamenta Mathematicae

On singular cut-and-pastes in the 3-space with applications to link theory.

Fujitsugu Hosokawa, Shin'ichi Suzuki (1995)

Revista Matemática de la Universidad Complutense de Madrid

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....

On some weak monomorphisms and weak epimorphisms of pro-HTop*.

I. Pop (1996)

Revista Matemática de la Universidad Complutense de Madrid

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.

On sprays and connections

Kozma, László (1990)

Proceedings of the Winter School "Geometry and Physics"

[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 S ( v ) = H ( v , v ) , v T M , locally G i ( x , y ) = y j Γ j i ( x , y ) , where G i and Γ j i express the semi-spray S and the connection map H, resp. In the linear case of H its geodesic spray S is quadratic: G i ( x , y ) = Γ j k i ( k ) y j y k . On the contrary, the homogeneity condition of S induces the relation for the compatible connection H, y j ( Γ j i μ t ) = t y j Γ j i , whence it follows not that H is linear, i.e. if a connection structure is compatible with a spray, then...

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