A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Classifies Morse boundaries of 3-manifold groups.
Develops sublinear Morse theory in symmetric spaces.
Inequalities for symplectic cohomology groups are derived.
In this paper we state and prove Morse type inequalities for Morse functions as well as for closed differential 1-forms. These inequalities involve delocalized Betti numbers. As an immediate consequence, we prove the vanishing of delocalized Betti numbers of manifolds fibering over the circle.
We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function. A rigidity result is also proved for the Floer complex of a hamiltonian defined on a closed symplectic manifold with $c_{1}|_{π_{2}(M)}=[ω]|_{π_{2}(M)…
Introduces a Morse complex on symplectic manifolds using gradient flows and proves its cohomology is independent of metrics and Morse functions.
We pursue the analogy of a framed flow category with the flow data of a Morse function. In classical Morse theory, Morse functions can sometimes be locally altered and simplified by the Morse moves. These moves include the Whitney trick which removes two oppositely framed flowlines between critical points of adjacent i…
Generalizes Floer homotopy via Morse-Bott theory.
We introduce Morse-type inequalities for a holomorphic circle action on a holomorphic vector bundle over a compact Kaehler manifold. Our inequalities produce bounds on the multiplicities of weights occurring in the twisted Dolbeault cohomology in terms of the data of the fixed points and of the symplectic reduction. Th…
We pose a conjecture about Morse-type integrals in nef (1,1) classes on compact Hermitian manifolds, and we show that it holds for semipositive classes, or when the manifold admits certain special Hermitian metrics.
New Morse theory for shapes at distances.
We give a new proof of the Morse Homology Theorem by constructing a chain complex associated to a Morse-Bott-Smale function that reduces to the Morse-Smale-Witten chain complex when the function is Morse-Smale and to the chain complex of smooth singular -cube chains when the function is constant. We show that the ho…
The paper introduces Morse theory for Lie groupoids and proves inequalities.
Study topological properties of foliations induced by closed 1-forms on orbifolds.
Study stabilizers of smooth functions on surfaces, focusing on Morse-Bott functions.
In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology-- for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology theory. As a preliminary we investigate functoriality in Morse homology. Functor…
We show that a Bott-Morse foliation in dimension 3 admits a linear, singular, Poisson structure of rank 2 with Bott-Morse singularities. We provide the Poisson bivectors for each type of singular component, and compute the symplectic forms of the characteristic distribution.
Researchers simplify the computation of diffeomorphism groups for Morse-Bott foliations.
The present paper contains an interpretation and generalization of Novikov's theory of Morse type inequalities for 1-forms in terms of Conley's theory for dynamical systems.
Let be a smooth closed orientable surface. Let be the space of Morse functions on having fixed number of critical points of each index, moreover at least critical points are labeled by different labels (enumerated). A notion of a skew cylindric-polyhedral complex, which generalizes the notion of a …
Transcendental holomorphic Morse inequalities aim at characterizing the positivity of transcendental cohomology classes of type . In this paper, we prove a weak version of Demailly's conjecture on transcendental Morse inequalities on compact Kähler manifolds. And as a consequence, we partially improve a result o…
In this paper we present the full details of the construction of a Morse-Floer type homology related to the super-quadratic perturbation of the Dirac-geodesic model. This homology is computed explicitly using a Leray-Serre type spectral sequence and this computation leads us to several existence results of Dirac-geodes…
Study on 4D Riemannian manifolds solves curvature problem.
Study Morse theory on loop spaces and Hecke algebras.
We study codimension one smooth foliations with Morse type singularities on closed ma-nifolds. We obtain a description of the manifold in case the number of centers in greater then the number of saddles. This result relies on and extends previous results of Reeb (for foliations having only centers) and Ells-Kuiper (for…
Geodesics spiral around compact subsets in CAT(0) spaces.
Study Morse-Novikov cohomology on foliated manifolds and prove Hodge theorem.
We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distingu…
Proves immediate transversality for conic singularities.
New example of hyperbolic 6-manifold with circle-valued Morse function.
We study codimension one (transversally oriented) foliations $\fa$ on oriented closed manifolds having non-empty compact singular set $\sing(\fa)$ which is locally defined by Bott-Morse functions. We prove that if the transverse type of $\fa$ at each singular point is a center and $\fa$ has a compact leaf with fini…
The paper characterizes subgroup stability via limit sets on the Morse boundary.
In Garside groups, axes of Morse elements are strongly contracting.
The works of Donaldson and Mark make the structure of the Seiberg-Witten invariant of 3-manifolds clear. It corresponds to certain torsion type invariants counting flow lines and closed orbits of a gradient flow of a circle-valued Morse map on a 3-manifold. We study these invariants using the Morse-Novikov theory and H…
Contractible diffeomorphism groups on lens spaces derived from Morse-Bott foliations.
Stability of Morse index for Yang-Mills connections in 4D.
In this paper, we study the prescribed -curvature problem on closed four-dimensional Riemannian manifolds when the total integral of the -curvature is a positive integer multiple of the one of the four-dimensional round sphere. This problem has a variational structure with a lack of compactness. Using some topolo…
Develops Morse homology with DG coefficients for manifolds and spaces.
Homotopy connectedness theorems for complex submanifolds of homogeneous spaces (sometimes referred to as theorems of Barth-Lefshetz type) have been established by a number of authors. Morse Theory on the space of paths lead to an elegant proof of homotopy connectedness theorems for complex submanifolds of Hermitian sym…
The study finds a special type of smooth function on connected sums of manifolds.
Study confirms conjecture on Hermitian manifolds with bounded mass.
Abstract Morse index theorem applied to various optimization problems.
Paper compares higher torsions and removes fiberwise Morse function assumption.
For a finitely generated group, there are two recent generalizations of the notion of a quasiconvex subgroup of a word-hyperbolic group, namely a stable subgroup and a Morse or strongly quasiconvex subgroup. Durham and Taylor defined stability and proved stability is equivalent to convex cocompactness in mapping class …
Study of diffeomorphisms groups on lens spaces with Morse-Bott foliations.
Minimal submanifolds in spheres can be produced via Clifford type minimal products, and their Morse indices and nullities are calculated.
We introduce a new type of boundary for proper geodesic spaces, called the Morse boundary, that is constructed with rays that identify the "hyperbolic directions" in that space. This boundary is a quasi-isometry invariant and thus produces a well-defined boundary for any finitely generated group. In the case of a prope…
The paper studies bifurcations in Lagrangian systems and geodesics.