We introduce the notion of cofoliation on a stack. A cofoliation is a change of the differentiable structure which amounts to giving a full representable smooth epimorphism. Cofoliations are uniquely determined by their associated Lie algebroids. Cofoliations on stacks arise from flat connections on groupoids. Connections on groupoids generalize connections on gerbes and bundles in a natural wa...

M. A. Al Shumrani Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Correspondence should be addressed to M. A. Al Shumrani, [email protected] Received 10 March 2010; Accepted 5 May 2010 Academic Editor: Mihai Putinar Copyright q 2010 M. A. Al Shumrani. This is an open access article distributed under the Creative Commons Attribution License,...

In any concrete category C the natural problem of whether epimorphisms are surjective maps arise, as well as the dual problem of whether the monomorphisms are injective maps. This type of problems have already been studied before in several well known categories: for example in [6] it is shown that the property of epimorphisms of being surjective holds in the categories of von Neumann algebras,...

Deformation theory requires solving Maurer-Cartan equation (MCE) associated to an DGLA (L-infinity algebra). The universal solution of [HS] is obtained iteratively, as a fixed point of a contraction, analogous to the Picard method. The role of the Kuranishi functor in this construction is emphasized. The parallel with Lie theory suggests that deformation theory is a higher “dimensional” version...

We show that every injective homological ring epimorphism f : R → S where SR has flat dimension at most one gives rise to a 1cotilting R-module and we give sufficient conditions under which the converse holds true. Specializing to the case of a valuation domain R, we illustrate a bijective correspondence between equivalence classes of injective homological ring epimorphisms originating in R and...

Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions B ⊆ A by H, are studied. Assuming that a lifted canonical map is a split epimorphism of modules of the (non-commutative) base algebra of H, relative injectivity of the H-comodule algebra A is related to the Galois property of the extension B ⊆ A and also to the equivalence of the category of relative Hopf...

Given a finitely presented group G and an epimorphism φ : G → Z Cochran and Harvey defined a sequence of invariants dn(G,φ) ∈ N0, n ∈ N0, which can be viewed as the degrees of higher–order Alexander polynomials. Cochran and Harvey showed that (up to a minor modification) this is a never decreasing sequence of numbers if G is the fundamental group of a 3–manifold with empty or toroidal boundary....

0.1. Related results. Krstić-McCool proved that GL3(A) is not finitely presented if there is an epimorphism from A to F [t] for some field F [Krs-Mc]. Suslin proved that SLn(A[t1, . . . , tk]) is generated by elemetary matrices if n ≥ 3, A is a regular ring, and K1(A) ∼= A× [Su]. GrunewaldMennicke-Vaserstein proved that Sp2n(A[t1, . . . , tk]) is generated by elementary matrices if n ≥ 2 and A ...

The Wahlquist-Estabrook prolongation method allows to obtain for some PDEs a Lie algebra that is responsible for Lax pairs and Bäcklund transformations of certain type. We study the Wahlquist-Estabrook algebra of the n-dimensional generalization of the Landau-Lifshitz equation and construct an epimorphism from this algebra onto an infinite-dimensional quasigraded Lie algebra L(n) of certain mat...

We exhibit new examples of double Kodaira fibrations by using finite Galois covers a product $\Sigma_b \times \Sigma_b$, where $\Sigma_b$ is smooth projective curve genus $b \geq 2$. Each cover obtained providing an explicit group epimorphism from the pure braid $\mathsf{P}_2(\Sigma_b)$ to some Heisenberg group. In this way, we are able show that every $b$ base fibration; moreover, number pairw...