We introduce the notion of stability of continuous homomorphisms of topological groups with respect to the compact-open topology on the space of all continuous functions between them and prove that the characters of any locally compact abelian group are stable in this sense. Using this notion we also generalize a global stability result on continuous homomorphisms between compact groups to a lo...

We define an infinite family of linearly independent, integer-valued smooth concordance homomorphisms. Our homomorphisms are explicitly computable and rely on local equivalence classes knot Floer complexes over the ring $\mathbb{F}[U, V]/(UV=0)$. compare our invariants to other coming from homology, discuss applications topologically slice knots, genus, unknotting number.

We present a framework for the complexity classification of parameterized counting problems that can be formulated as the summation over the numbers of homomorphisms from small pattern graphs H1, . . . ,H` to a big host graph G with the restriction that the coefficients correspond to evaluations of the Möbius function over the lattice of a graphic matroid. This generalizes the idea of Curticape...

Document archives contain large amounts of data to which sophisticated queries are applied. The size of archives and the complexity of evaluating queries makes the use of parallelism attractive. The use of semantically-based markup such as SGML makes it possible to represent documents and document archives as data types. We present a theory of trees and tree homomorphisms, modelling structured ...

Let X be a hypergroup. In this paper, we study the homomorphisms on certain subspaces of L(X)* which are weak*-weak* continuous.

Communication between information systems is considered as an important issue in granular computing. The concept of homomorphism is an effective mathematical tool to study information exchange between information systems. This paper provides a study on some basic properties of covering information systems and decision systems under homomorphisms. First, we define consistent functions related to...

Homomorphisms between relational structures are not only fundamental mathematical objects, but are also of great importance in an applied computational context. Indeed, constraint satisfaction problems, a wide class of algorithmic problems that occur in many different areas of computer science such as artificial intelligence or database theory, may be viewed as asking for homomorphisms between ...

We extend certain homomorphisms defined on the higher Torelli subgroups of the mapping class group to crossed homomorphisms defined on the entire mapping class group. In particular, for every k ≥ 2, we construct a crossed homomorphism ǫk which extends Morita’s homomorphism τ̃k to the entire mapping class group. From this crossed homomorphism we also obtain a crossed homomorphism extending the kt...