In the study of equisingularity of isolated singularities we have the classical theorem of Briançon, Speder and Teissier which states that a family of isolated hypersurface singularities is Whitney equisingular if and only if the μ∗sequence for a hypersurface is constant in the family. In this paper we generalize to non-isolated hypersurface singularities. By assuming non-contractibility of str...

We associate a contractible “outer space” to any free product of groups G = G1∗· · ·∗Gq . It equals Culler-Vogtmann space when every Gi is Z, McCulloughMiller space when no Gi is Z. Our proof of contractibility is based on Skora’s idea of deforming morphisms between trees. Using the action of Out(G) on this space, we show that Out(G) has finite virtual cohomological dimension, or is VFL (it has...

Many topological properties of the whole family of stable polynomials and matrices have been studied in a number of publications (see e.g., [1,3–7,11,12]). The present paper continues these investigations with the aim of strengthening these results in the sense that instead of simple-connectivity we show stronger property of contractibility of the various families of stable matrices from this p...

We compute the global dimension function $\mathrm{gldim}$ on principal component $\mathrm{Stab}^{\dag}(\mathbb{P}^2)$ of space Bridgeland stability conditions $\mathbb{P}^2$. It admits $2$ as minimum value and preimage $\mathrm{gldim}^{-1}(2)$ is contained in closure $\bar{\mathrm{Stab}^{\mathrm{Geo}}(\mathbb{P}^2)}$ subspace consisting geometric conditions. show that $\mathrm{gldim}^{-1}[2,x)$...

This paper continues the investigation of the rst author begun in part one. The hereditary properties of n-homomorphism amenability for Banach algebras are investigated and the relations between n-homomorphism amenability of a Banach algebra and its ideals are found. Analogous to the character amenability, it is shown that the tensor product of two unital Banach algebras is n-homomorphism amena...

The topological approach to social choice was developed by Graciela Chichilnisky in the beginning of the eighties. The main result in this area (known as the resolution of the topological social choice paradox) shows that a space of preferences admits of a continuous, anonymous, and unanimous aggregation rule for every number of individuals if and only if the space is contractible. Furthermore,...