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Pedro Ontaneda

Publications and source records attributed to Pedro Ontaneda.

17 recordsLinked to original sources
arXiv2022

Intrinsic Rank in CAT(0) Spaces

Let $X$ be a proper, geodesically complete CAT(0) space which satisfies Chen and Eberlein's duality condition. We show the existence of a strong notion of rank for $X$ by proving that the parallel sets $P_v$ of geodesics $v$ in $X$ are generically flat. More precisely, let $GX$ be the space of parametrized unit-speed geodesics in $X$. There is a unique $k$ and a dense $G_δ$ set $\mathcal{A}$ in $GX$ such that $P_v$ is isometric to flat Euclidean space $\mathbb{R}^k$, for all $v \in \mathcal{A}$. It follows that $\mathbb{R}^k$ isometrically embeds in $P_v$ for every $v \in GX$.

math.MG↗
arXiv2015

New partially hyperbolic dynamical systems I

We propose a new method for constructing partially hyperbolic diffeomorphisms on closed manifolds. As a demonstration of the method we show that there are simply connected closed manifolds that support partially hyperbolic diffeomorphisms.

math.DS↗
arXiv2015

Sphere Bundles with 1/4-pinched Fiberwise Metrics

We prove that all smooth sphere bundles that admit fiberwise 1/4-pinched metrics are induced bundles of vector bundles, so their structure groups reduce from the diffeomorphism group of the sphere to the orthogonal group. This result implies the existence of many smooth n-sphere bundles over a k-sphere that do not support strictly 1/4-pinched positively curved Riemannian metrics on their fibers.

math.GT↗
arXiv2006

Three Applications of Instanton Numbers

We use instanton numbers to: (i) stratify moduli of vector bundles, (ii) calculate relative homology of moduli spaces and (iii) distinguish curve singularities.

math-ph↗
arXiv2004

Cocompact Proper CAT(0) Spaces

This paper is about geometric and topological properties of a proper CAT(0) space $X$ which is cocompact - i.e. which has a compact generating domain with respect to the full isometry group. It is shown that geodesic segments in $X$ can "almost" be extended to geodesic rays. A basic ingredient of the proof of this geometric statement is the topological theorem that there is a top dimension $d$ in which the compactly supported integral cohomology of $X$ is non-zero. It is also proved that the boundary-at-infinity of $X$ (with the cone topology) has Lebesgue covering dimension $d-1$. It is not assumed that there is any cocompact discrete subgroup of the isometry group of $X$; however, a corollary for that case is that "the dimension of the boundary" is a quasi- isometry invariant of CAT(0) groups. (By contrast, it is known that the topological type of the boundary is not unique for a CAT(0) group.)

math.MG↗