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This thesis is concerned with the definition and the study of properties of homotopic Hopf-Galois extensions in the category Ch 0 k of chain complexes over a field k, equipped with its projective model structure. Given a differential graded k-Hopf algebra H of finite type, we define a homotopic H-Hopf-Galois extension to be a morphism ' : B ! A of augmented H-comodule dg-k-algebras, where B is ...

In this paper, analytic solutions of two-dimensional coupled Burgers' equations are obtained by the Homotopy analysis and the Homotopy Pad$acute{e}$ methods. The obtained approximation by using Homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by $[m,m]$ Homotopy Pad$acute{e...

Given some type of fibration on a 4-manifold X with a torus regular fiber T , we may produce a new 4-manifold XT by performing torus surgery on T . There is a natural way to extend the fibration to XT , but a multiple fiber (nongeneric) singularity is introduced. We construct explicit generic fibrations (with only indefinite fold singularities) in a neighborhood of this multiple fiber. As an ap...

For spaces localized at 2, the classical EHP fibrations [1, 13] ΩS S ΩS ΩS play a crucial role for the computations of the homotopy groups of the spheres [16, 25]. The EHP-fibrations for (p− 1)-cell complexes for p > 2 are given in this article. These fibrations can be regarded as the odd prime analogue of the classical EHP-fibrations by considering the spheres as 1-cell complexes for p = 2. So...

We present a way of constructing a Quillen model structure on a full subcategory of an elementary topos, starting with an interval object with connections and a certain dominance. The advantage of this method is that it does not require the underlying topos to be cocomplete. The resulting model category structure gives rise to a model of homotopy type theory with identity types, Σand Π-types, a...