Luis Javier Hernández Paricio

EXACT SEQUENCES AND CLOSED MODEL CATEGORIES

For every closed model category with zero object, Quillen gave the construction of Eckman-Hilton and Puppe sequences. In this paper, we remove the hypothesis of the existence of zero object and construct (using the category over the initial object or the category under the final object) these sequences for unpointed model categories. We illustrate the power of this result in abstract homotopy theory given some interesting applications to group cohomology and exterior homotopy groups.For every closed model category with zero object, Quillen gave the construction of Eckman-Hilton and Puppe sequences. In this paper, we remove the hypothesis of the existence of zero object and construct (using the category over the initial object or the category under the final object) these sequences for unpointed model categories. We illustrate the power of this result in abstract homotopy theory given some interesting applications to group cohomology and exterior homotopy groups.

A completion construction for continuous dynamical systems

In this work we use the theory of exterior spaces to construct a~

Bivariate Newton-Raphson method and toroidal attraction basins

\check{C}_{0}^\mathbf{r}

Graphical representations for the homogeneous bivariate Newton's method

-completion and a

Closed model categories for uniquely S -divisible spaces

\check{C}_{0}^\mathbf{l}

Self-overlays and symmetries of Julia sets of expanding maps

-completion of a dynamical system. If

Prolongations, Suspensions and Telescopes

X

Homotopy Categories for Simply Connected Torsion Spaces

is a~flow, we construct canonical maps

Plotting basins of end points of rational maps with Sage

X\to \check{C}_{0}^\mathbf{lr(X)

Combinatorial koszul homology, computations and applications

and