• Corpus ID: 237491523

Localization and flexibilization in symplectic geometry

  title={Localization and flexibilization in symplectic geometry},
  author={Oleg Lazarev and Zachary Sylvan and Hirokazu Tanaka},
We introduce the critical Weinstein category the result of stabilizing the category of Weinstein sectors and inverting subcritical morphisms and construct localizing ‘P-flexibilization’ endofunctors indexed by collections P of Lagrangian disks in the stabilization of a point T ∗D0. Like the classical localization of topological spaces studied by Quillen, Sullivan, and others, these functors are homotopy-invariant and localizing on algebraic invariants like the Fukaya category. Furthermore… 

Figures from this paper



Geometric and algebraic presentations of Weinstein domains

We prove that geometric intersections between Weinstein handles induce algebraic relations in the wrapped Fukaya category, which we use to study the Grothendieck group. We produce a surjective map

Altering symplectic manifolds by homologous recombination

We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a variety and a

Generation for Lagrangian cobordisms in Weinstein manifolds

We prove that Lagrangian cocores and Lagrangian linking disks of a stopped Weinstein manifold generate the Lagrangian cobordism infinity-category. As a geometric consequence, we see that any brane

A stable ∞-category of Lagrangian cobordisms

Arboreal singularities in Weinstein skeleta

We study the singularities of the isotropic skeleton of a Weinstein manifold in relation to Nadler’s program of arboreal singularities. By deforming the skeleton via homotopies of the Weinstein

Sectorial descent for wrapped Fukaya categories

We develop a set of tools for doing computations in and of (partially) wrapped Fukaya categories. In particular, we prove (1) a descent (cosheaf) property for the wrapped Fukaya category with respect

Covariantly functorial wrapped Floer theory on Liouville sectors

We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors,

On partially wrapped Fukaya categories

We define a new class of symplectic objects called ‘stops’, which, roughly speaking, are Liouville hypersurfaces in the boundary of a Liouville domain. Locally, these can be viewed as pages of a

Prime-localized Weinstein subdomains

For any high-dimensional Weinstein domain and finite collection of primes, we construct a Weinstein subdomain whose wrapped Fukaya category is a localization of the original wrapped Fukaya category

Rational homotopy theory

1 The Sullivan model 1.1 Rational homotopy theory of spaces We will restrict our attention to simply-connected spaces. Much of this goes through with nilpotent spaces, but this will keep things