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Ingrid Membrillo-Solis

Publications and source records attributed to Ingrid Membrillo-Solis.

4 recordsLinked to original sources
arXiv2019

Topology and geometry of molecular conformational spaces and energy landscapes

Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding problem, drug design and the structure activity relationship problem. Despite their relevance, configuration spaces of molecules are only partially understood. In this paper we discuss both theoretical and computational approaches to the configuration spaces of molecules and their associated energy landscapes. Our mathematical approach shows that when symmetries of the molecules are taken into account, configuration spaces of molecules give rise to certain principal bundles and orbifolds. We also make use of a variety of geometric and topological tools for data analysis to study the topology and geometry of these spaces.

q-bio.QM↗
arXiv2019

On gauge groups over high dimensional manifolds and self-equivalences of $H$-spaces

Let $Y$ be a pointed space and let $\mathcal E(Y^r)$ be the group of based self-equivalences of $Y^r$, $r\geq 2$. For $Y$ a homotopy commutative $H$-group we construct a subgroup $\mathcal E_{\mathrm{Mat}}(Y^r)$ of $\mathcal E(Y^r)$ which has a group structure isomorphic to either $GL_r(\mathbb Z)$, or $GL_r(\mathbb Z_d)$, $d\geq 2$. We classify principal bundles over connected sums of $q$-sphere bundles over $n$-spheres and use the group $\mathcal E_{\mathrm{Mat}}(Y^r)$ to obtain homotopy decompositions of their gauge groups. Using these decompositions we give an integral classification, up to homotopy, of the gauge groups of principal $SU(2)$-bundles over certain 2-connected 7-manifolds with torsion-free homology.

math.AT↗
arXiv2019

Homotopy types of gauge groups related to $S^3$-bundles over $S^4$

Let $M_{l,m}$ be the total space of the $S^3$-bundle over $S^4$ classified by the element $lσ+mρ\in{π_4(SO(4))}$, $l,m\in\mathbb Z$. In this paper we study the homotopy theory of gauge groups of principal $G$-bundles over manifolds $M_{l,m}$ when $G$ is a simply connected simple compact Lie group such that $π_6(G)=0$. That is, $G$ is one of the following groups: $SU(n)$ $(n\geq4)$, $Sp(n)$ $(n\geq2)$, $Spin(n)$ $(n\geq5)$, $F_4$, $E_6$, $E_7$, $E_8$. If the integral homology of $M_{l,m}$ is torsion-free, we describe the homotopy type of the gauge groups over $M_{l,m}$ as products of recognisable spaces. For any manifold $M_{l,m}$ with non-torsion-free homology, we give a $p$-local homotopy decomposition, for a prime $p\geq 5$, of the loop space of the gauge groups.

math.AT↗