相关论文: Simplicity of augmentations of codimension 1 germs…

We prove several results regarding the simplicity of germs and multigerms obtained via the operations of augmentation, simultaneous augmentation and concatenation and generalised concatenation. We also give some results in the case where…

For function germs $g:(\mathbb C^n,0)\to (\mathbb C,0)$ it is well known that $1\leq\frac{\mu(g)}{\tau(g)}$ and it has recently been proved by Liu that $\frac{\mu(g)}{\tau(g)}\leq n$. We give an upper bound for the codimension of map-germs…

We generalise the operations of augmentation and concatenations in order to obtain multigerms of analytic (or smooth) maps $(\mathbb K^n,S)\rightarrow(\mathbb K^p,0)$ with $\mathbb K=\mathbb C$ or $\mathbb R$ from monogerms and some special…

We study liftable vector fields of smooth map-germs. We show how to obtain the module of liftable vector fields of any map-germ of finite singularity type from the module of liftable vector fields of a stable unfolding of it. As an…

We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of…

For finite permutation groups, simplicity of the augmentation submodule is equivalent to $2$-transitivity over the field of complex numbers. We note that this is not the case for transformation monoids. We characterize the finite…

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…

We prove that the linearization of a germ of holomorphic map of the type $F_\lambda(z)=\lambda(z+O(z^2))$ has a $ C^1$--holomorphic dependence on the multiplier $\lambda$. $C^1$--holomorphic functions are $ C^1$--Whitney smooth functions,…

A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. In this paper, we study the embedded homology as well as the homology of the (lower-)associated simplicial complexes for hypergraphs. We…

In a previous paper the authors elaborated notions and technique which could be applied to compute such invariants of polynomials as Euler characteristics of fibres and zeta-functions of monodromy transformations associated with a…

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…

A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary…

A set of Morse numbers is associated to a holomorphic function germ with stratified isolated singularity, extending the classical Milnor number to the setting of a singular base space.

We consider the problem of extending germs of plane holomorphic foliations to foliations of compact surfaces. We show that the germs that become regular after a single blow up and admit meromorphic first integrals can be extended, after…

We show that the weight four modular graph functions that contribute to the integrand of the t_8 t_8 D^4 R^4 term at one loop in heterotic string theory do not require regularization, and hence the integrand is simple. This is unlike the…

We consider Legendrian links and tangles in $J^1S^1$ and $J^1[0,1]$ equipped with Morse complex families over a field $\mathbb{F}$ and classify them up to Legendrian cobordism. When the coefficient field is $\mathbb{F}_2$ this provides a…

In this work we define some map-germs, called elementary joins, for the purpose of producing new ${\mathcal A}$-finite map-germs from them. In particular, we describe a general form of an ${\mathcal A}$-finite monomial map from…

In studies of smooth maps with good differential topological conditions such as immersions, embeddings, Morse functions and their higher dimensional versions including fold maps and application to geometry, especially algebraic and…

Closed (and simply-connected) manifolds whose dimensions are larger than 4 are central geometric objects in classical algebraic topology and differential topology. They have been classified via algebraic and abstract objects. On the other…

Closed (and simply-connected) manifolds whose dimensions are greater than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed…