Displaying similar documents to “Hochschild homology of finite dimensional algebras.”

The Vietoris system in strong shape and strong homology

Bernd Günther (1992)

Fundamenta Mathematicae


We show that the Vietoris system of a space is isomorphic to a strong expansion of that space in the Steenrod homotopy category, and from this we derive a simple description of strong homology. It is proved that in ZFC strong homology does not have compact supports, and that enforcing compact supports by taking limits leads to a homology functor that does not factor over the strong shape category. For compact Hausdorff spaces strong homology is proved to be isomorphic to Massey's homology. ...

Induced mappings of homology decompositions

Martin Arkowitz (1998)

Banach Center Publications


We give conditions for a map of spaces to induce maps of the homology decompositions of the spaces which are compatible with the homology sections and dual Postnikov invariants. Several applications of this result are obtained. We show how the homotopy type of the (n+1)st homology section depends on the homotopy type of the nth homology section and the (n+1)st homology group. We prove that all homology sections of a co-H-space are co-H-spaces, all n-equivalences of the homology decomposition...

An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

H.-Ch. Graf von Bothmer, Wolfgang Ebeling, Xavier Gómez-Mont (2008)

Annales de l’institut Fourier


Let ( V , 0 ) be a germ of a complete intersection variety in n + k , n > 0 , having an isolated singularity at 0 and X be the germ of a holomorphic vector field having an isolated zero at 0 and tangent to V . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space n + k we give a formula for the homological index in terms of local linear algebra.