Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can ...

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can ...

The best understood 3-manifolds are Haken 3-manifolds; these are manifolds that are irreducible and contain incompressible surfaces. One approach to 3-manifolds is to try to generalize the notion of an incompressible surface. Essential laminations and mapped-in π1-injective surfaces have both been used with some success as substitutes for incompressible surfaces, yielding theorems which apply t...

This paper gives a proof that the universal cover of a closed 3-manifolds built from three π1-injective handlebodies is homeomorphic to R .

In the category of operator spaces, that is, subspaces of the bounded linear operators B(H) on a complex Hilbert space H together with the induced matricial operator norm structure, objects are equivalent if they are completely isometric, i.e., if there is a linear isomorphism between the spaces which preserves this matricial norm structure. Since operator algebras, that is, subalgebras of B(H)...

and Applied Analysis 3 2. α-Times Regularized Resolvent Family Throughout this paper, X is a complex Banach space, and we denote by B X the algebra of all bounded linear operators on X. Let A be a closed densely defined operator on X, let D A and R A be its domain and range, respectively, and let α ∈ 0, 2 , C ∈ B X be injective. Define ρC A : {λ ∈ C : λ − A is injective and R C ⊂ R λ − A }. Let...

Let $R$ be a ring, $n$ an non-negative integer and $d$ positive or $\infty$. A right $R$-module $M$ is called \emph{$(n,d)^*$-projective} if ${\rm Ext}^1_R(M, C)=0$ for every $n$-copresented $C$ of injective dimension $\leq d$; ring \emph{right $(n,d)$-cocoherent} with $id(C)\leq d$ $(n+1)$-copresented; $(n,d)$-cosemihereditary} whenever $0\rightarrow C\rightarrow E\rightarrow A\rightarrow 0$ e...

Let k be a field. Given two finite-dimensional right comodules N andM over a k–coalgebra C, the k–vector spaces ExtC(N,M) need not to be finite-dimensional. This is due to the fact that the injective right comodules appearing in the minimal injective resolution of M need not to be of finite dimension or even quasi-finite. The obstruction here is that factor comodules of quasi-finite comodules a...

The main purpose of this paper is to investigate almost periodic properties of various classes of (a, k)-regularized C-resolvent families in Banach spaces. We contemplate the work of many other authors working in this field, giving also some original contributions and applications. In general case, (a, k)regularized C-resolvent families under our considerations are degenerate and their subgener...