arXiv subjects

Hector Cordova Bulens

Publications and source records attributed to Hector Cordova Bulens.

3 recordsLinked to original sources

arXiv2015

Rational model of the configuration space of two points in a simply connected closed manifold

Let $M$ be a simply connected closed manifold of dimension $n$. We study the rational homotopy type of the configuration space of 2 points in $M$, $F(M,2)$. When $M$ is even dimensional, we prove that the rational homotopy type of $F(M,2)$ depends only on the rational homotopy type of $M$. When the dimension of $M$ is odd, for every $x\in H^{n-2} (M, \mathbb{Q})$, we construct a commutative differential graded algebra $C(x)$. We prove that for some $x \in H^{n-2} (M; \mathbb{Q})$, $C(x)$ encodes completely the rational homotopy type of $F(M,2)$. For some class of manifolds, we show that we can take $x=0$.

math.AT↗

arXiv2015

Rational models of the complement of a subpolyhedron in a manifold with boundary

Let W be a compact simply connected triangulated manifold with boundary and $K \subset W$ be a subpolyhedron. We construct an algebraic model of the rational homotopy type of the complement $W \setminus K$ out of a model of the map of pairs $(K, K \cap \partial W) \to (W,\partial W)$ under some high codimension hypothesis. We deduce the rational homotopy invariance of the configuration space of two points in a compact manifold with boundary under 2-connectedness hypotheses. Also, we exhibit nice explicits models of these configuration spaces for a large class of compact manifolds.

math.AT↗

arXiv2015

Pretty rational models for Poincaré duality pairs

We prove that a large class of Poincaré duality pairs admit rational models (in the sense of Sullivan) of a particularly nice form associated to some Poincaré duality CDGA. These models have applications in particular to the construction of rational models of configuration spaces in compact manifolds with boundary.

math.AT↗