76 citations · 308 across the 22 of their papers we have counts for
28 papers
Filtered cospans and interlevel persistence with boundary conditions
Michael Usher
We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respec…
Abstract interlevel persistence for Morse-Novikov and Floer theory
Michael Usher
We develop a general algebraic framework involving "Poincaré--Novikov structures" and "filtered matched pairs" to provide an abstract approach to the barcodes associated to the hom…
Local rigidity, contact homeomorphisms, and conformal factors
Michael Usher
We show that if the image of a Legendrian submanifold under a contact homeomorphism (i.e. a homeomorphism that is a -limit of contactomorphisms) is smooth then it is Legendria…
Local rigidity, symplectic homeomorphisms, and coisotropic submanifolds
Michael Usher
We introduce the notion of a point on a locally closed subset of a symplectic manifold being "locally rigid" with respect to that subset, prove that this notion is invariant under…
Symplectic Banach-Mazur distances between subsets of C^n
Michael Usher
Following proposals of Ostrover and Polterovich, we introduce and study "coarse" and "fine" versions of a symplectic Banach-Mazur distance on certain open subsets of …
Infinite staircases in the symplectic embedding problem for four-dimensional ellipsoids into polydisks
Michael Usher
We study the symplectic embedding capacity function for ellipsoids into dilates of polydisks as both and vary through . For $…
Symplectically knotted codimension-zero embeddings of domains in
Jean Gutt, Michael Usher
We show that many toric domains in admit symplectic embeddings into dilates of themselves which are knotted in the strong sense that there is no symplectomorphism of…
Graphicality, C^0 convergence, and the Calabi homomorphism
Michael Usher
Consider a sequence of compactly supported Hamiltonian diffeomorphisms of an exact symplectic manifold, all of which are "graphical" in the sense that their graphs are identi…
Persistent homology and Floer-Novikov theory
Michael Usher, Jun Zhang
We construct "barcodes" for the chain complexes over Novikov rings that arise in Novikov's Morse theory for closed one-forms and in Floer theory on not-necessarily-monotone symplec…
Observations on the Hofer distance between closed subsets
Michael Usher
We prove the elementary but surprising fact that the Hofer distance between two closed subsets of a symplectic manifold can be expressed in terms of the restrictions of Hamiltonian…
On Certain Lagrangian Submanifolds of and
Joel Oakley, Michael Usher
We consider various constructions of monotone Lagrangian submanifolds of , and quadric hypersurfaces of . In and we show that s…
Hofer geometry and cotangent fibers
Michael Usher
For a class of Riemannian manifolds that include products of arbitrary compact manifolds with manifolds of nonpositive sectional curvature on the one hand, or with certain positive…
Linking and the Morse complex
Michael Usher
For a Morse function f on a compact oriented manifold M, we show that f has more critical points than the number required by the Morse inequalities if and only if there exists a ce…
Submanifolds and the Hofer norm
Michael Usher
Chekanov showed that the Hofer norm on the Hamiltonian diffeomorphism group of a geometrically bounded symplectic manifold induces a nondegenerate metric on the orbit of any compac…
Hofer's metrics and boundary depth
Michael Usher
We show that if (M,ω) is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer's metric o…
Many closed symplectic manifolds have infinite Hofer-Zehnder capacity
Michael Usher
We exhibit many examples of closed symplectic manifolds on which there is an autonomous Hamiltonian whose associated flow has no nonconstant periodic orbits (the only previous expl…
Deformed Hamiltonian Floer theory, capacity estimates, and Calabi quasimorphisms
Michael Usher
We develop a family of deformations of the differential and of the pair-of-pants product on the Hamiltonian Floer complex of a symplectic manifold (M,ω) which upon passing to homol…
Duality in filtered Floer-Novikov complexes
Michael Usher
We prove that a certain bilinear pairing (analagous to the Poincare-Lefschetz intersection pairing) between filtered sub- and quotient complexes of a Floer-type chain complex and o…
Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds
Michael Usher
We assign to each nondegenerate Hamiltonian on a closed symplectic manifold a Floer-theoretic quantity called its "boundary depth," and establish basic results about how the bounda…
The sharp energy-capacity inequality
Michael Usher
Using the Oh-Schwarz spectral invariants and some arguments of Frauenfelder, Ginzburg, and Schlenk, we show that the π_1-sensitive Hofer-Zehnder capacity of any subset of a closed…
Floer homology in disc bundles and symplectically twisted geodesic flows
Michael Usher
We show that if K: P \to R is an autonomous Hamiltonian on a symplectic manifold (P,Ω) which attains 0 as a Morse-Bott nondegenerate minimum along a symplectic submanifold M, and i…
Spectral numbers in Floer theories
Michael Usher
The chain complexes underlying Floer homology theories typically carry a real-valued filtration, allowing one to associate to each Floer homology class a spectral number defined as…
Kodaira dimension and symplectic sums
Michael Usher
Modulo trivial exceptions, we show that smoothly nontrivial symplectic sums of symplectic 4-manifolds along surfaces of positive genus are never rational or ruled, and we enumerate…
Minimality and symplectic sums
Michael Usher
Let X_1, X_2 be symplectic 4-manifolds containing symplectic surfaces F_1,F_2 of identical positive genus and opposite squares. Let Z denote the symplectic sum of X_1 and X_2 along…