Related papers: On simple $Z_2$-invariant and corner function germ…

Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…

A Group category is a spherical category whose simple objects are invertible. The invariant of Turaev-Viro with this particular category is in fact the invariant of Dijkgraaf-Witten whose the group and the 3-cocycle is given by the simple…

We consider algebras defined over a complete, local and noetherian ground ring. They are gentle algebras in case the ground ring is a field. The unbounded homotopy category of complexes of projective modules is considered. Complexes with…

This submission is a PhD dissertation. It constitutes the summary of the author's work concerning the relations between cohomology rings of algebraic varieties and rings of functions on zero schemes and fixed point schemes. It includes the…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

We study the nilpotent part $N'$ of a pseudo-periodic automorphism $h$ of a real oriented surface with boundary $\Sigma$. We associate a quadratic form $Q$ defined on the first homology group (relative to the boundary) of the surface…

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by…

For each integral homology sphere $Y$, a function $\Gamma_Y$ on the set of integers is constructed. It is established that $\Gamma_Y$ depends only on the homology cobordism of $Y$ and it recovers the Fr{\o}yshov invariant. A relation…

Characterizing face-number-related invariants of a given class of simplicial complexes has been a central topic in combinatorial topology. In this regard, one of the well-known invariants is $g_2$. Let $K$ be a normal $3$-pseudomanifold…

We associate to any irreducible germ S of complex quasi-ordinary hypersurface an analytically invariant semigroup. We deduce a direct proof (without passing through their embedded topological invariance) of the analytical invariance of the…

In this paper we study the bi-Lipschitz triviality of deformations of an analytic function germ $f$ defined on a germ of an analytic variety $(X, 0)$ in $\mathbb C^n$. We introduce the notion of strongly rational $\mathscr R_X$-bi-Lipschitz…

We prove that every suitable $4$-manifold with $b_1=0$ and with an embedded Riemann surface of genus $2$ is of simple type. We find a relationship between the basic classes of two of these $4$-manifolds and those of the connected sum along…

We introduce a class of normal complex spaces having only mild sin-gularities (close to quotient singularities) for which we generalize the notion of a (analytic) fundamental class for an analytic cycle and also the notion of a relative…

Perez-Marco proved the existence of non-trivial totally invariant connected compacts called hedgehogs near the fixed point of a nonlinearizable germ of holomorphic diffeomorphism. We show that if two nonlinearisable holomorphic germs with a…

We construct the equivariant analytic lattice cohomology associated with the analytic type of a complex normal surface singularity whenever the link is a rational homology sphere. It is the categorification of the equivariant geometric…

We study conjugacy classes of germs of non-flat diffeomorphisms of the real line fixing the origin. Based on the work of Takens and Yoccoz, we establish results that are sharp in terms of differentiability classes and order of tangency to…

Two measures of how near an arbitrary function between groups is to being a homomorphism are considered. These have properties similar to conjugates and commutators. The authors show that there is a rich theory based on these structures,…

We define an Isometry germ at any given event $x$ of space-time as a vector field $\xi$ defined in a neighborhood of $x$ such that the Lie derivative of both the metric and the Riemannian connection are zero at this event. Two isometry…

If V is a representation of a linear algebraic group G, a set S of G-invariant regular functions on V is called separating if the following holds: If two elements v,v' from V can be separated by an invariant function, then there is an f…

In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…