The first two authors have recently defined RabinowitzFloer homology groups RFH∗(M,W ) associated to an exact embedding of a contact manifold (M, ξ) into a symplectic manifold (W,ω). These depend only on the bounded component V of W \ M . We construct a long exact sequence in which symplectic cohomology of V maps to symplectic homology of V , which in turn maps to Rabinowitz-Floer homology RFH∗...

By using surgery techniques, we compute Floer homology for certain classes of integral homology 3-spheres homology cobordant to zero. We prove that Floer homology is two-periodic for all these manifolds. Based on this fact, we introduce a new integer valued invariant of integral homology 3-spheres. Our computations suggest its homology cobordism invariance.

We adapt Bar-Natan's scanning algorithm for fast computations in (even) Khovanov homology to odd homology. use a mapping cone construction instead of tensor product, which allows us deal efficiently with the more complicated sign assignments theory. The has been implemented computer program. also determine 3-strand torus links.

We consider the following situation: a field k, a commutative k-algebra R and a left R-module M. Since R is commutative, M may also be considered as an R-R bimodule with the same operation on each side (such modules are often termed symmetric). With these assumptions we have the Harrison (co-) homology groups Harr,(R, M) (Harr*(R, M)), the Hochschild (co-) homology groups Hoch, (R, M) (Hoch*(R,...

We use the Dolbeault cohomology to investigate Koszul–Brylinski homology on holomorphic Poisson manifolds. obtain Leray–Hirsch theorem for Hochschild and Mayer–Vietoris sequence, Künneth homology. In particular, we show some relations of homologies around a blow-up transformation general case (not necessarily compact) by our previous works cohomology.

In this paper, the authors study further properties and applications of weighted homology persistent homology. The Mayer-Vietoris sequence generalized Bockstein spectral for are introduced. For applications, show an algorithm to construct a filtration simplicial complexes from network. They also prove theorem calculate mod p2 provided with some information on p

We prove that the skein categories of Walker–Johnson-Freyd satisfy excision. This allows us to conclude are k-linear factorisation homology and taking free cocompletion recovers locally finitely presentable homology. An application this is algebra a punctured surface related any quantum group with generic parameter gives quantisation associated character variety.

Every Brieskorn homology sphere (p; q; r) is a double cover of the 3{sphere ramiied over a Montesinos knot k(p; q; r). We relate Floer homology of (p; q; r) to certain invariants of the knot k(p; q; r), among which are the knot signature and the Jones polynomial. We also deene an integer valued invariant of integral homology 3{spheres which agrees with the {invariant of W. Neu-mann and L. Siebe...

In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a para...