We examine the cokernel of canonical homomorphism from trivial source ring a finite group to $p$-rational complex characters. use Boltje and Co\c{s}kun's theory fibered biset functors determine structure cokernel. An essential tool in determination this is Bouc's rational $p$-biset functors.

We are interested in those bundles on P that admits a resolution of the form 0 → C ⊗ E φ −→ C t ⊗ F → C → 0. In this paper we prove that, under suitable conditions on E, F , a generic bundle with this form is either simple, or canonically decomposable. As applications we provide an easy criterion for the stability of such bundles on P and we prove the stability of all Steiner exceptional bundle...

In this paper we construct new obstructions for the surjectivity of the Johnson homomorphism of the automorphism group of a free group. We also determine the structure of the cokernel of the Johnson homomorphism for degree 2 or 3.

Abstract. We introduce the concept of a morphism between coloured nets. Our definition generalizes Petris definition for ordinary nets. A morphism of coloured nets maps the topological space of the underlying undirected net as well as the kernel and cokernel of the incidence map. The kernel are flows along the transitionbordered fibres of the morphism, the cokernel are classes of markings of th...

We prove that for the free group of rank two F cokernel homomorphism to its Baumslag rationalization ? Bau(F) is not abelian. Moreover, this contains a subgroup countable rank. This answers question Emmanuel Farjoun.

Let F be a field of characteristic zero and let ft,n be the stabilization homomorphism from the nth integral homology of SLt(F ) to the nth integral homology of SLt+1(F ). We prove the following results: For all n, ft,n is an isomorphism if t ≥ n+ 1 and is surjective for t = n, confirming a conjecture of C-H. Sah. fn,n is an isomorphism when n is odd and when n is even the kernel is isomorphic ...

Let φ : Rm → Rd be a map of free modules over a commutative ring R. Fitting’s Lemma shows that the “Fitting ideal,” the ideal of d × d minors of φ, annihilates the cokernel of φ and is a good approximation to the whole annihilator in a certain sense. In characteristic 0 we define a Fitting ideal in the more general case of a map of graded free modules over a Z/2graded skew-commutative algebra a...

The well-known notion of crossed module of groups is raised in this paper to the categorical level supported by the theory of categorical groups. We construct the cokernel of a categorical crossed module and we establish the universal property of this categorical group. We also prove a suitable 2-dimensional version of the kernelcokernel lemma for a diagram of categorical crossed modules. We th...

In this paper, we extend the constructions of Boava and Exel to present C∗-algebra associated with an injective endomorphism a group finite cokernel as partial algebra consequently crossed product. With representation, another way study such C∗-algebras, only using tools from products.