58 citations · 80 across the 8 of their papers we have counts for
11 papers
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…
Twisted generating functions and the nearby Lagrangian conjecture
Mohammed Abouzaid, Sylvain Courte, Stéphane Guillermou +1
We prove that, for closed exact embedded Lagrangian submanifolds of cotangent bundles, the homomorphism of homotopy groups induced by the stable Lagrangian Gauss map vanishes. In p…
Generating Functions in and the Hatcher-Waldhausen map
Thomas Kragh
In this paper, we construct a generating function quadratic at infinity for any exact Lagrangian in that equals outside a compact set. Such a Lagrang…
Simple Homotopy Equivalence of Nearby Lagrangians
Mohammed Abouzaid, Thomas Kragh
Given a closed exact Lagrangian in the cotangent bundle of a closed smooth manifold, we prove that the projection to the base is a simple homotopy equivalence.
Homotopy equivalence of nearby Lagrangians and the Serre spectral sequence
Thomas Kragh
We construct using relatively basic techniques a spectral sequence for exact Lagrangians in cotangent bundles similar to the one constructed by Fukaya, Seidel, and Smith. That spec…
Lagrangian exotic spheres
Tobias Ekholm, Thomas Kragh, Ivan Smith
Let k>2. We prove that the cotangent bundles of oriented homotopy (2k-1)-spheres S and S' are symplectomorphic only if the classes defined by S and S' agree up to sign in the quoti…
On the immersion classes of nearby Lagrangians
Mohammed Abouzaid, Thomas Kragh
We show that the transfer map on Floer homotopy types associated to an exact Lagrangian embedding is an equivalence. This provides an obstruction to representing isotopy classes of…
Fibrancy of Symplectic Homology in Cotangent Bundles
Thomas Kragh
We describe how the result in [1] extends to prove the existence of a Serre type spectral sequence converging to the symplectic homology SH_*(M) of an exact Sub-Liouville domain M…
Parametrized Ring-Spectra and the Nearby Lagrangian Conjecture
Thomas Kragh
We prove that any closed connected exact Lagrangian manifold L in a connected cotangent bundle T*N is up to a finite covering space lift a homology equivalence. We prove this by co…
Orientations and Connective Structures on 2-vector Bundles
Thomas Kragh
In work by Ausoni, Dundas and Rognes a half magnetic monopole is discovered and describes an obstruction to creating a determinant K(ku) \to ku*. In fact it is an obstruction to cr…
The Viterbo Transfer as a Map of Spectra
Thomas Kragh
Let and be two smooth manifolds of the same dimension. Let be an exact Lagrange embedding. We denote the free loop space of by . C. Viterbo cons…