arXiv subjects

Daniel Álvarez-Gavela

Publications and source records attributed to Daniel Álvarez-Gavela.

2 recordsLinked to original sources

arXiv2026

Weinstein manifolds as cotangent buildings

We introduce the framework of cotangent buildings to complement and refine that of Weinstein handlebodies. While Weinstein handlebodies are suitable for a ``bottom-up" analysis of the Weinstein structure, cotangent buildings also enable a ``top down" analysis. Further, cotangent buildings include a precise control over the interaction of any subcollection of the various building blocks, each of which is modeled on the cotangent bundle of a manifold with corners. Our main result is that any Weinstein manifold is Weinstein homotopic to one admitting the structure of a cotangent building.

math.SG↗

arXiv2025

Normal invariant of nearby Lagrangians via twisted derivative

Let $L$ and $M$ be closed, connected, smooth manifolds and let $L \hookrightarrow T^*M$ be an exact Lagrangian embedding. The induced map $L \to M$ is known by earlier work to be a homotopy equivalence. We show that the associated normal invariant $M \to G/O$ factors through a map $B(\mathcal{T},\mathcal{Q}) \to G/O$ which is a twisted version of the Waldhausen derivative $\mathcal{T} \to G$ on the space $\mathcal{T}$ of tubes. Further, we show that this twisted derivative map itself factors though a map $B(G/O) \to G/O$ which is a twisted version of the $S$-duality map $BG \to G$. In particular we deduce that the normal invariant of the homotopy equivalence $L \to M$ is 2-torsion.

math.SG↗