The concept of motivic integration was invented by Kontsevich to show that birationally
equivalent Calabi-Yau manifolds have the same Hodge numbers. He constructed a certain …

The notion of integration with respect to the Euler characteristic and its generalizations are
discussed: integration over the infinite-dimensional spaces of arcs and functions, motivic …

We unify and generalize formulas obtained by Campillo, Delgado and Gusein-Zade in their
series of articles. Positive results are established for rational and minimally elliptic …

Assume that is a connected negative definite plumbing graph, and that the associated
plumbed 3-manifold M is a rational homology sphere. We provide two new combinatorial …

We provide several results on splice-quotient singularities:(1) a combinatorial expression of
the dimension of the first cohomology of all 'natural'line bundles (involving the Seiberg …

We study the analytic and topological invariants associated with complex normal surface
singularities. Our goal is to provide topological formulae for several discrete analytic …

The lattice cohomology of a plumbed 3-manifold M associated with a connected negative
definite plumbing graph is an important tool in the study of topological properties of M and in …

In previous papers, the authors computed the Poincaré series of some (multi-index)
filtrations on the ring of germs of functions on a rational surface singularity. These Poincaré …

We construct the analytic lattice cohomology associated with the analytic type of any
complex normal surface singularity. It is the categorification of the geometric genus of the …

A multi-index filtration on the ring of germs of functions can be described by its Poincaré
series. We consider a finer invariant (or rather two invariants) of a multi-index filtration than …