13 citations · 20 across the 11 of their papers we have counts for
13 papers
The crosscut poset
Miguel Ottina
We introduce a new combinatorial invariant, which we call crosscut poset, that is finer than the crosscut complex. We exhibit many applications of the crosscut poset which include…
The crosscut poset and the fixed point property
Ana Gargantini, Miguel Ottina
We introduce two novel ideas related to the crosscut poset and give many examples of application of these ideas to the fixed point property.
Homology of posets with functor coefficients and its relation to Khovanov homology of knots
Nicolás Cianci, Miguel Ottina
We study homology groups of posets with functor coefficients and apply our results to give a novel approach to study Khovanov homology of knots and related homology theories.
Fibrations between finite topological spaces
Nicolás Cianci, Miguel Ottina
We study Hurewicz fibrations between finite T--spaces from a combinatorial viewpoint and give strong conditions that a continuous map between finite T--spaces must satisfy…
A new tool to study the fixed point property of finite posets
Ana Gargantini, Miguel Ottina
We develop a novel tool to study the fixed point property of finite posets using a topological approach. Our tool is a construction which turns out to induce an endofunctor of the…
Fiber bundles over Alexandroff spaces
Nicolás Cianci, Miguel Ottina
We introduce a topological variant of the Grothendieck construction which serves to represent every fiber bundle over an Alexandroff space. Using this result we give a classificati…
A combinatorial characterization of Hurewicz cofibrations between finite topological spaces
Nicolás Cianci, Miguel Ottina
We characterize the Hurewicz cofibrations between finite topological spaces, that is, the continuous functions between finite topological spaces that have the homotopy extension pr…
Smallest homotopically trivial non-contractible spaces
Nicolás Cianci, Miguel Ottina
We characterize the homotopically trivial non-contractible topological spaces with the minimum number of points.
Poset splitting and minimality of finite models
Nicolás Cianci, Miguel Ottina
We develop a novel technique, which we call poset splitting, that allows us to solve two open problems regarding minimality of finite models of spaces: the nonexistence of a finite…
On homology of finite topological spaces
Nicolás Cianci, Miguel Ottina
We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a compl…
An A-based cofibrantly generated model category
Miguel Ottina
We develop a cofibrantly generated model category structure in the category of topological spaces in which weak equivalences are A-weak equivalences and such that the generalized C…
A-homology, A-homotopy and spectral sequences
Miguel Ottina
Given a CW-complex A we define an `A-shaped' homology theory which behaves nicely towards A-homotopy groups allowing the generalization of many classical results. We also develop a…
A geometric decomposition of spaces into cells of different types
Gabriel Minian, Miguel Ottina
We develop the theory of CW(A)-complexes, which generalizes the classical theory of CW-complexes, keeping the geometric intuition of J.H.C. Whitehead's original theory. We obtain t…