7 citations · 19 across the 13 of their papers we have counts for
14 papers
Framed bordism of Lagrangian homotopy spheres via generating functions
Daniel Alvarez-Gavela
This note combines a result of Bökstedt and Waldhausen concerning the so-called derivative map on tubes with the existence theorem for generating functions of tube type for nearby…
Weinstein manifolds as cotangent buildings
Daniel Álvarez-Gavela, Yakov Eliashberg, David Nadler
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…
Normal invariant of nearby Lagrangians via twisted derivative
Mohammed Abouzaid, Daniel Álvarez-Gavela, Sylvain Courte +1
Let and be closed, connected, smooth manifolds and let be an exact Lagrangian embedding. The induced map is known by earlier work to be a…
On arborealization, Maslov data, and lack thereof
Daniel Alvarez-Gavela, Tim Large, Abigail Ward
For a Weinstein manifold, we compare and contrast the properties of admitting an arboreal skeleton and admitting Maslov data. Both properties are implied by the existence of a pola…
Flexibility of singularities and beyond
Daniel Alvarez-Gavela
We survey a selection of Yasha Eliashberg's contributions to the philosophy of the h-principle, with a focus on the simplification of singularities and its applications.
Caustics of Lagrangian homotopy spheres with stably trivial Gauss map
Daniel Alvarez-Gavela, David Darrow
For each positive integer , we give a geometric description of the stably trivial elements of the group . In particular, we show that all such elements admit repres…
Arboreal models and their stability
Daniel Alvarez-Gavela, Yakov Eliashberg, David Nadler
This is the first in a series of papers by the authors on the arborealization program. The main goal of the paper is the proof of uniqueness of arboreal models, defined as the clos…
Positive arborealization of polarized Weinstein manifolds
Daniel Alvarez-Gavela, Yakov Eliashberg, David Nadler
Let be a Weinstein manifold. We show that the existence of a global field of Lagrangian planes in is equivalent to the existence of a positive arboreal skeleton for the We…
Geomorphology of Lagrangian ridges
Daniel Alvarez-Gavela, Yakov Eliashberg, David Nadler
We prove an "h-principle without pre-conditions" for the elimination of tangencies of a Lagrangian submanifold with respect to a Lagrangian distribution. The main result states tha…
A Legendrian Turaev torsion via generating families
Daniel Alvarez-Gavela, Kiyoshi Igusa
We introduce a Legendrian invariant built out of the Turaev torsion of generating families. This invariant is defined for a certain class of Legendrian submanifolds of 1-jet spaces…
The simplification of singularities of Lagrangian and Legendrian fronts
Daniel Alvarez-Gavela
We establish a full principle (close, relative, parametric) for the simplification of singularities of Lagrangian and Legendrian fronts. More precisely, we prove that if…
Refinements of the holonomic approximation lemma
Daniel Alvarez-Gavela
The holonomic approximation lemma of Eliashberg and Mishachev is a powerful tool in the philosophy of the principle. By carefully keeping track of the quantitative geometry beh…
Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms
Daniel Alvarez-Gavela, Victoria Kaminker, Asaf Kislev +7
Given a symplectic surface of genus , we show that the free group with two generators embeds into every asymptotic cone of , w…
Gaussian curvature in codimension > 1
Daniel Alvarez-Gavela
The Gaussian curvature is a fundamental geometric quantity discovered by Gauss in the case of surfaces embedded in . One can naturally extend the definition of th…