We study the relationship between a homological capacity $$c_{\mathrm {SH}^+}(W)$$ for Liouville domains W defined using positive symplectic homology and existence of periodic orbits Hamiltonian systems on W: if is non-zero, then yields finite upper bound to $$\pi _1$$ -sensitive Hofer–Zehnder relative its skeleton certain class diffeomorphisms has infinitely many non-trivial contractible point...

This paper introduces a new idea in the unital involutive Banach algebras and its closed subset. aims to study cohomology theory of operator algebra. We will algebra as an applied example algebra, be denoted by . The definitions cyclic, simplicial, dihedral group src=image/13426521_01.gif> introduced. presented definition src=image/13426521_14.gif>-relative that i...

We find strong necessary conditions on the f -vectors, Betti sequences, and relative Betti sequence of a pair of simplicial complexes. We also present an example showing that these conditions are not sufficient. If only the difference between two Betti sequences is specified, and not the individual Betti sequences, then the characterization is complete, and the characterization of all pairs of ...

Let X be a compact metric space. By results of Brown, Douglas and Fillmore, [BDF2], the K-homology of X is realized by Ext(X), the equivalence classes of unital and essential extensions of C(X) by the compact operators K on a separable infinite dimensional Hilbert space H , or equivalently, the equivalence classes of unital and injective ∗-homomorphisms C(X) → Q, where Q = L(H)/K is the Calkin ...

Lecture 1 (Pflaum): Title: Relative cohomology and its pairings Relative cyclic cohomology theory and its pairings turned out to be a powerful tool to explain crucial properties of certain invariants in global analysis such as for example the divisor flow. In this talk, the homological foundations for pairings in relative cyclic cohomology will be explained. Moreover, the relative Chern-charact...