Let / be a holomorphic mapping between compact complex manifolds. We give a criterion for / to have unobstructed deformations, i.e. for the local moduli space of / to be smooth: this says, roughly speaking, that the group of infinitesimal deformations of f, when viewed as a functor, itself satisfies a natural lifting property with respect to infinitesimal deformations. This lifting property is ...

(1b) Question. For which pairs (C0,H) does a lift exist? Note that the lifting problem for C0 is formally smooth. However we will see that in general the lifting problem for (C0,H) can be obstructed; in some cases a lifting does not exist, in several cases ramification in R is needed to make a lifting possible. In order to have a positive answer to this question it suffices to consider the case...

We extend the path lifting property in homotopy theory for topological spaces to bitopological semigroups and we show and prove its role in the C(ℵ)-fibration property. We give and prove the relationship between the C(ℵ)-fibration property and an approximate fibration property. Furthermore, we study the pullback maps for C(ℵ)-fibrations.

We study the uniqueness of minimal liftings of cut-generating functions obtained from maximal lattice-free polyhedra. We prove a basic invariance property of unique minimal liftings for general maximal lattice-free polyhedra. This generalizes a previous result by Basu, Cornuéjols and Köppe [BCK12] for simplicial maximal lattice-free polytopes, thus completely settling this fundamental question ...

Lifting properties for Banach spaces are studied. An alternate version of the lifting property due to Lindenstrass and Tzafriri leads a new geometric called quotient pairs (X, J), with J proximinal in X. Several necessary sufficient conditions hold given.

Group valued edge labellings λ of a Bratteli diagram B give rise to a skew-product Bratteli diagram B(λ) on which the group acts. The quotient by the group action of the associated dynamics can be a nontrivial extension of the dynamics of B. We exhibit a Bratteli diagram for this quotient and construct a morphism to B with unique path lifting property. This is shown to be an isomorphism for the...

Finitely-hollow lifting and hollow-weak modules are two generalizations of hollow module which is a weaker version module. In this paper, we have defined another generalization hollow-lifting namely finitely-hollow-weak (f-hollow-weak lifting) Various properties been seen found that, it not closed under quotients summands in general, so sufficient conditions provided f-hollow-weak property inhe...