相关论文: Disentanglements of corank 2 map-germs: two exampl…

We consider the possible disentanglements of holomorphic map germs $f \colon (\mathbb C^n,0) \to (\mathbb C^N,0)$, $n < N$, with nonisolated locus of instability $\operatorname{Inst}(f)$. The aim is to achieve lower bounds for their…

We consider $\mathcal{A}$-finite map germs $f$ from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{2n},0)$. First, we show that the number of double points that appears in a stabilization of $f$, denoted by $d(f)$, can be calculated as the length of…

We study corank one $A$-finite germs $f:(\mathbb{R}^n,0)\rightarrow (\mathbb{R}^{n+1},0)$ and their complexifications. More precisely, we study when these germs provide good real pictures of the complex germs, i.e., when there is a real…

We produce new examples supporting the Mond conjecture which can be stated as follows. The number of parameters needed for a miniversal unfolding of a finitely determined map-germ from $n$-space to $(n+1)$-space is less than (or equal to if…

We study a moduli stratum of A-orbits of plane-to-plane germs of corank 2 with codimension 3. We describe explicitly the bifurcation diagram of its topologically A-versal unfolding. Two geometric applications to parabolic objects are…

We give a simple way to study the isotypical components of the homology of simplicial complexes with actions of finite groups, and use it for Milnor fibers of ICIS. We study the homology of images of mappings $f_t$ that arise as…

We construct all codimension 1 multi-germs of maps (k^n,T)-->(k^p,0) with n > p-2, (n,p) nice dimensions, k = R or C, by augmentation and concetenation operations, starting from mon-germs (|T|=1). As an application, we prove general results…

For a complex analytic map f from n-space to p-space with n<p and with an isolated instability at the origin, the disentanglement of f is a local stabilization of f that is analogous to the Milnor fibre for functions. For mono-germs it is…

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…

In this paper we study the homology and cohomology of confguration spaces of two distinct particles on a graph. Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra of the…

We compute the cohomology groups of the spaces of colorings of cycles, i.e., of the prodsimplicial complexes Hom(C_m,K_n). We perform the computation first with Z_2, and then with integer coefficients. The main technical tool is to use…

In this work we investigate the topological information captured by the Euler obstruction of a map, $f:(X,0)\to (\mathbb{C}^{2},0)$, with $(X,0)$ a germ of a complex $d$-equidimensional singular space, with $d > 2$, and its relation with…

In this work, we consider a quasi-homogeneous, corank $1$, finitely determined map germ $f$ from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^3,0)$. We consider the invariants $m(f(D(f))$ and $J$, where $m(f(D(f))$ denotes the multiplicity of the…

We study germs of analytic maps $f:(X,S)\rightarrow(\mathbb{C}^p,0)$, when $X$ is an ICIS of dimension $n<p$. We define an image Milnor number, generalizing Mond's definition, $\mu_I(X,f)$ and give results known for the smooth case such as…

We give a formula to count the number of $D_4$ singularities in a stable frontal perturbation of a corank $2$ wave front singularity $f\colon (\mathbb{C}^3,0) \to (\mathbb{C}^4,0)$ using Mond's method of stable perturbations of map germs.…

In this paper we calculate the homology of configuration spaces of $n$ points on a circle, subject to the condition that two pre-determined points are included in the configuration. We make use of discrete Morse theory both to determine the…

We consider a corank $1$, finitely determined, quasi-homogeneous map germ $f$ from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^3,0)$. We describe the embedded topological type of a generic hyperplane section of $f(\mathbb{C}^2)$, denoted by…

Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological…

We study the topology of the space of harmonic maps from $S^2$ to \CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for…

We compute the homology of the matching complex $M(\Gamma)$, where $\Gamma$ is the complete hypergraph on $n\geq 2$ vertices, and analyse the $S_n$-representations carried by this homology. These results are achieved using standard…