Definition 1.2. The module of relative differential forms of B over A is a Bmodule ΩB/A, together with an A-derivation d : B → ΩB/A satisfying the following universal property: for any B-module M and for any A-derivation d : B → M , there exists a unique B-module homomorphism f : ΩB/A → M such that d ′ = f ◦d. If DerA(B,M) denotes the set of all A-derivations from B into M , then we have a natu...

In this talk we will discuss some examples of graph homomorphisms. More precisely, the graph parameters which can be represented by counting the graph homomorphisms. The main reference is Section 2 in [2].

For a graph G, let     max : is an edge cut of b G D D G  . For graphs G and H, a map     :V G V H   is a graph homomorphism if for each   e uv E G   ,       u v E H    . In 1979, Erdös proved by probabilistic methods that for p ≥ 2 with

A graph homomorphism is a vertex map which carries edges from a source graph to edgesin a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem(MAX H -COL) are edge-weighted graphs G and the objective is to find a subgraph of G that hasmaximal total edge weight, under the condition that the subgraph has a homomorphism to H ;note that for H = Kk th...

In the red corner, topological K-theory! The study of stable equivalences of vector bundles over a topological space, and the engine behind Bott periodicity, a result whose reverberations are felt throughout algebraic topology. In the blue corner, modular representation theory! The story of representations in positive characteristic, where the CDE triangle powers applications in group theory an...

We give two generalizations of the Atiyah-Bott-Berline-Vergne lo-calization theorem for the equivariant cohomology of a torus action: 1) replacing the torus action by a compact connected Lie group action, 2) replacing the manifold having a torus action by an equivariant map. This provides a systematic method for calculating the Gysin homomorphism in ordinary co-homology of an equivariant map. A...

Let X be a compact metric space which is locally absolutely retract and let ϕ: C(X) → C(Y,M(n)) be a unital homomorphism, where Y is a compact metric space with dim Y ≤ 2. It is proved that there exists a sequence of n continuous maps α(i,m): Y → X (i = 1,2,…,n) and a sequence of sets of mutually orthogonal rank-one projections {p(1,m),p(2,m),…,p(n,m)} C(Y,M(n)) such that [see formula]. This is...

In a recent paper [1], a systematic construction of integrable Hamiltonians with coalgebra symmetry has been proposed. Such procedure can be applied to any Poisson coalgebra (A,∆) with generators Xi, i = 1, . . . , l and Casimir element C(X1, . . . , Xl) as follows. Let us consider the N -th coproduct ∆(Xi) of the generators and the m-th order (2 ≤ m ≤ N) coproducts ∆(m)(C) of the Casimir opera...

A dimension group is an ordered abelian that inductive limit of a sequence simplicial groups, and stationary such in which the homomorphism same at every stage. If simple then up to scalar multiplication it admits unique trace (positive real-valued homomorphism), but short exact associated this need not split. In earlier paper, Handelman [J. Operator Theory 6 (1981), pp. 55–74] described these ...