22 citations · 26 across the 30 of their papers we have counts for
21 papers · 1 filter
Global Fukaya category II: applications
Yasha Savelyev
To paraphrase, part I constructs a bundle of categories given the input of a Hamiltonian fibration over a smooth manifold. Here we show that this bundle is generally…
Strict contactomorphisms are scarce
Yong-Geun Oh, Yasha Savelyev
The notion of non-projectible contact forms on a given compact manifold is introduced by the first-named author in [Ohb], the set of which he also shows is a residual subset of…
Quantum Maslov classes
Yasha Savelyev
We give a construction of ``quantum Maslov characteristic classes'', generalizing to higher dimensional cycles the Hu-Lalonde-Seidel morphism. We also state a conjecture extending…
Elliptic curves in lcs manifolds and metric invariants
Yasha Savelyev
We study invariants defined by count of charged, elliptic -holomorphic curves in locally conformally symplectic manifolds. We use this to define -valued deformation…
A remark on deformation of Gromov non-squeezing
Yasha Savelyev
Let be as in the classical Gromov non-squeezing theorem, and let . We first conjecture that the Gromov non-squeezing phenomenon persists for…
Locally conformally symplectic deformation of Gromov non-squeezing
Yasha Savelyev
We prove one deformation theoretic extension of the Gromov non-squeezing phenomenon to structures, or locally conformally symplectic structures, which suitably generalize bot…
Pseudoholomoprhic curves on the -fication of contact manifolds
Yong-Geun Oh, Yasha Savelyev
For each contact diffeomorphism of , we equip its mapping torus with a \emph{locally conformal symplectic} form of Banyaga's type, which we call t…
A conformal symplectic Weinstein conjecture
Yasha Savelyev
We introduce a direct generalization of the Weinstein conjecture to closed, Lichnerowicz exact, locally conformally symplectic manifolds, (for short $\lcs$ manifolds). This conject…
Gromov-Witten theory of a locally conformally symplectic manifold
Yasha Savelyev
We initiate here the study of Gromov-Witten theory of locally conformally symplectic manifolds or $\lcs$ manifolds, $\lcsm$'s for short, which are a natural generalization of both…
K-theoretic invariants of Hamiltonian fibrations
Yasha Savelyev, Egor Shelukhin
We introduce new invariants of Hamiltonian fibrations with values in the suitably twisted K-theory of the base. Inspired by techniques of geometric quantization, our invariants ari…
On the Hofer geometry injectivity radius conjecture
Yasha Savelyev
We verify here some variants of topological and dynamical flavor of the injectivity radius conjecture in Hofer geometry, Lalonde-Savelyev \cite{citeLalondeSavelyevOntheinjectivityr…
Floer theory and topology of
Yasha Savelyev
We say that a fixed point of a diffeomorphism is non-degenerate if 1 is not an eigenvalue of the linearization at the fixed point. We use pseudo-holomorphic curves techniques to pr…
Global Fukaya category II: singular connections, quantum obstruction theory, and other applications
Yasha Savelyev
In part I, using the theory of -categories, we constructed a natural ``continuous action'' of on the Fukaya category of a closed monotone symp…
Morse theory for the Hofer length functional
Yasha Savelyev
Following \cite{citeSavelyevVirtualMorsetheoryonHam.}, we develop here a connection between Morse theory for the (positive) Hofer length functional $L: Ω\text {Ham…
Global Fukaya category I
Yasha Savelyev
Let denote the Frechet Lie group of Hamiltonian symplectomorphisms of a monotone symplectic manifold . Let be the -nerve of the Fu…
Proof of the index conjecture in Hofer geometry
Yasha Savelyev
Let be a non-degenerate Ustilovsky geodesic in generated by . We give a simple proof of a generalization of the conjecture stated in \cite{virtmorse}, relating…
On configuration spaces of stable maps
Yasha Savelyev
We study here some aspects of the topology of the space of smooth, stable, genus 0 curves in a Riemannian manifold , i.e. the Kontsevich stable curves, which are not necessarily…
Gromov K-area and jumping curves in CP^n
Yasha Savelyev
We give here some extensions of Gromov's and Polterovich's theorems on $\karea$ of , particularly in the symplectic and Hamiltonian context. Our main methods inv…
Bott periodicity and stable quantum classes
Yasha Savelyev
We use Bott periodicity to relate previously defined quantum classes to certain "exotic Chern classes" on . This provides an interesting computational and theoretical framework…
Virtual Morse theory on
Yasha Savelyev
We relate previously defined quantum characteristic classes to Morse theoretic aspects of the Hofer length functional on $\ls$. As an application we prove a theorem which can be in…
Quantum characteristic classes and the Hofer metric
Yasha Savelyev
Given a closed monotone symplectic manifold , we define certain characteristic cohomology classes of the free loop space with values in , and the…