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Now showing items 1-10 of 15

#### On the geometry of strongly flat semigroups and their generalizations

(2018-09-18)

Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and ...

#### Multiplicity and degree as bi‐Lipschitz invariants for complex sets

(Journal of Topology, 2018-08-29)

We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz
transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz ...

#### Némethi’s division algorithm for zeta-functions of plumbed 3-manifolds

(Bulletin of the London Mathematical Society, 2018-08-27)

A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite
plumbing 3-manifold has been proposed by earlier work of the authors. It is provided by a
special decomposition of the zeta-function ...

#### Some classes of homeomorphisms that preserve multiplicity and tangent cones

(2018-08-19)

In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ...

#### On Zariski’s multiplicity problem at infinity

(Proceedings of the American Mathematical Society, 2018-08-14)

We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are bi-Lipschitz homeomorphic at infinity must have the same degree. More specifically, ...

#### Hölder equivalence of complex analytic curve singularities

(Bulletin of the London Mathematical Society, 2018-08-06)

We prove that if two germs of irreducible complex analytic curves at $0\in\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\alpha<1$ such that those germs are not $\alpha$-H\"older ...

#### Semialgebraic CMC surfaces in $\mathbb{R}^3$ with singularities

(2018-06-30)

In this paper we present a classification of a class of semialgebraic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016 (complete reference is in the paper), we ...

#### Singularities in Geometry and Topology

(2018-06-18)

This thesis consists of two different topics that are not related. The thesis has two different and independent parts that can be read in any order. The purpose of this work is to study two topics in singularity theory: ...

#### Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3-manifolds

(2018-06)

Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg-Witten invariant can be computed as the ‘periodic constant’ of the topological multivariable Poincaré series (zeta ...