Patrick Massot
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View article: Formalising the $h$-principle and sphere eversion
Formalising the $h$-principle and sphere eversion Open
In differential topology and geometry, the h-principle is a property enjoyed by certain construction problems. Roughly speaking, it states that the only obstructions to the existence of a solution come from algebraic topology. We describe …
View article: Holonomic Approximation Through Convex Integration
Holonomic Approximation Through Convex Integration Open
Convex integration and the holonomic approximation theorem are two well-known pillars of flexibility in differential topology and geometry. They may each seem to have their own flavor and scope. The goal of this paper is to bring some new …
View article: Formalising perfectoid spaces
Formalising perfectoid spaces Open
Perfectoid spaces are sophisticated objects in arithmetic geometry introduced by Peter Scholze in 2012. We formalised enough definitions and theorems in topology, algebra and geometry to define perfectoid spaces in the Lean theorem prover.…
View article: Contactomorphism groups and Legendrian flexibility
Contactomorphism groups and Legendrian flexibility Open
We explain a connection between the algebraic and geometric properties of groups of contact transformations, open book decompositions, and flexible Legendrian embeddings. The main result is that, if a closed contact manifold $(V, ξ)$ has a…
View article: On the contact mapping class group of Legendrian circle bundles
On the contact mapping class group of Legendrian circle bundles Open
In this paper, we determine the group of contact transformations modulo contact isotopies for Legendrian circle bundles over closed surfaces of non-positive Euler characteristic. These results extend and correct those presented by the firs…
View article: Quantitative Darboux theorems in contact geometry
Quantitative Darboux theorems in contact geometry Open
This paper begins the study of relations between Riemannian geometry and\ncontact topology in any dimension and continues this study in dimension 3.\nSpecifically we provide a lower bound for the radius of a geodesic ball in a\ncontact man…