Abstract We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of singular subanalytic germs. The main novelty our approach is allow “moderately discontinuous” chains, are specially advantageous for capturing the subtleties outer phenomena. Our invariant finitely generated graded abelian group any and homomorphisms ....

The determination of cyclic (co)homology of a given algebra is a quite important and difficult problem. Let us briefly recall some of the results obtained that are somehow related to our paper. The cyclic homology of group algebras over fields of characteristic 0 was computed by Burghelea, [3]. For a complete algebraic proof of Burghelea’s result the reader is referred to [19], while a relative...

We study the effect of edge contractions on simplicial homology because these contractions have turned out to be useful in various applications involving topology. It was observed previously that contracting edges that satisfy the so called link condition preserves homeomorphism in low dimensional complexes, and homotopy in general. But, checking the link condition involves computation in all d...

The deoxyribonucleic acid homologies of Mycoplasma laidlawii type A and type B, M. pulmonis (#47 and #63), and M. hominis were determined by membrane methodology. The homology data revealed a difference in genome size between M. laidlawii type A and type B. This difference also held with stringent conditions of annealing (high temperature). Little or negligible homology was shown to exist betwe...

Nigel Higson and John Roe Abstract: We connect the assembly map in C∗-algebra K-theory to rigidity properties for relative eta invariants that have been investigated by Mathai, Keswani, Weinberger and others. We give a new and conceptual proof of Keswani’s theorem that whenever the C∗-algebra assembly map is an isomorphism, the relative eta invariants associated to the signature operator are ho...

Floer homology is a powerful variational technique used in Symplectic Geometry to derive a Morse type theory for the Hamiltonian action functional. In two and three dimensional dynamics the topological structures of braids and links can used to distinguish between various types of periodic orbits. Various classes of braids are introduced and Floer type invariants are defined. The definition and...