We give an [Formula: see text] algorithm for computing the text]-dimensional persistent homology of a filtration clique complexes cyclic graphs on vertices. This is nearly quadratic in number vertices text], and therefore large improvement upon traditional algorithm, which cubic simplices dimension at most hence running time text]. Our applies, example, to Vietoris–Rips points sampled from curv...

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski as a special case and provides an equivariant extension of the local cyclic theory developped by Puschnigg. As a main result we construct a multip...