Related papers: Germs in a poset

This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…

We prove that every not necessarily bounded poset P=(P,\le,') with an antitone involution can be extended to a residuated poset E(P)=(E(P),\le,\odot,\rightarrow,1) where x'=x\rightarrow0 for all x\in P. If P is a lattice with an antitone…

A question of B. Teissier, inspired by a previous problem of R. Thom, asks whether for any germ of complex analytic hypersurface there exists a germ of complex algebraic hypersurface with the same topological type. Up to now only the case…

In this paper we introduce new classes of gluing of complex analytic spaces germs, called weakly large, large and strongly large. We give a description of their Poincar\'e series and, as applications, we give numerical criteria to determine…

Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for "many" objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general framework under which it is possible to…

S.Janson [Poset limits and exchangeable random posets, Combinatorica 31 (2011), 529--563] defined limits of finite posets in parallel to the emerging theory of limits of dense graphs. We prove that each poset limit can be represented as a…

For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some…

We prove that every finitely generated residually finite group $G$ can be embedded in a finitely generated branch group $\Gamma$ such that two elements in $G$ are conjugate in $G$ if and only if they are conjugate in $\Gamma$. As an…

Semistability at infinity is an asymptotic property of finitely presented groups that is needed in order to effectively define the fundamental group at infinity for a 1-ended group. It is an open problem whether or not all finitely…

We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by a similar property of the fundamental group of the complement of an irreducible hypersurface in the complex projective…

The interleaving distance, although originally developed for persistent homology, has been generalized to measure the distance between functors modeled on many posets or even small categories. Existing theories require that such a poset…

We prove that every finite distributive lattice is isomorphic to a final segment of the d.c.e. Turing degrees (i.e., the degrees of differences of computably enumerable sets). As a corollary, we are able to infer the undecidability of the…

Suppose that a complex manifold M is locally embedded into a higher-dimensional neighbourhood as a submanifold. We show that, if the local neighbourhood germs are compatible in a suitable sense, then they glue together to give a global…

We give necessary and sufficient conditions of infinite determinacy for smooth function germs whose critical locus contains a given set. This set is assumed to be the zero variety X of some analytic map germ having maximal rank on a dense…

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various…

We prove that in a semi-bounded o-minimal expansion of an ordered group every non-empty open definable set is a finite union of open cells.

We give an elementary combinatorial proof of the following fact: Every real or complex analytic complete intersection germ X is equisingular -- in the sense of the Hilbert-Samuel function -- with a germ of an algebraic set defined by…

Let F be a family of subsets of {1,2,...,n}. The width-degree of an element x in at least one member of F is the width of the family {U in F | x in U}. If F has maximum width-degree at most k, then F is locally k-wide. Bounds on the size of…

In this note we give a self-contained proof of a fundamental statement in the study of cosheaves over a poset. Specifically, if a functor has domain a poset and co-domain a co-complete category, then the left Kan extension of that functor…

Let G be a graph with vertices V and edges E. Let F be the union-closed family of sets generated by E. Then F is the family of subsets of V without isolated points. Theorem: There is an edge e belongs to E such that |{U belongs to F | e…