Related papers: Contact spectral invariants and persistence

In her PhD thesis Milin developed an equivariant version of the contact homology groups constructed by Eliashberg, Kim and Polterovich and used it to prove an equivariant contact non-squeezing theorem. In this article we re-obtain the same…

Based on the contact Hamiltonian Floer theory established by Will J. Merry and the second author that applies to any admissible contact Hamiltonian system $(M, \xi = \ker \alpha, h)$, where $h$ is a contact Hamiltonian function on a…

We define a class of invariants, which we call homological invariants, for persistence modules over a finite poset. Informally, a homological invariant is one that respects some homological data and takes values in the free abelian group…

In this paper we propose a theory of contact invariants and open string invariants, which are generalizations of the relative invariants. We introduce two moduli spaces $\bar{\mathcal{M}}_{A}(M^{+},C,g,m+\nu,{\bf y},{\bf…

We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…

The combinatorial interpretation of the persistence diagram as a M\"obius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Transform of a geometric complex as a representation of a…

The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…

This paper associates a persistence module to a contact vector field $X$ on the ideal boundary of a Liouville manifold. The persistence module measures the dynamics of $X$ on the region $\Omega$ where $X$ is positively transverse to the…

This paper presents a systematic quantitative study of contact rigidity phenomena based on the contact Hamiltonian Floer theory established by Merry-Uljarevi\'c. Our quantitative approach applies to arbitrary admissible contact Hamiltonian…

We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology, and introduce new invariants to study these equivalence classes. These new invariants are as simple, but more discerning…

By general case we mean methods able to process simplicial sets and chain complexes not of finite type. A filtration of the object to be studied is the heart of both subjects persistent homology and spectral sequences. In this paper we…

In this article, the author defines an invariant of rational homology 3-spheres equipped with a contact structure as an element of a cohomotopy set of the Seiberg-Witten Floer spectrum as defined in Manolescu (2003). Furthermore, in light…

We give an explicit expression for the contact loci of hyperplane arrangements and show that their cohomology rings are combinatorial invariants. We also give an expression for the restricted contact loci in terms of Milnor fibers of…

A method to apply and visualize persistent homology of time series is proposed. The method captures persistent features in space and time, in contrast to the existing procedures, where one usually chooses one while keeping the other fixed.…

A new characterization is provided for the class of compact rank-one symmetric spaces. Such spaces are the only symmetric spaces of compact type for which the standard vector field on their sphere bundles is Killing with respect to some…

In recent times a great amount of progress has been achieved in symplectic and contact geometry, leading to the development of powerful invariants of 3-manifolds such as Heegaard Floer homology and embedded contact homology. These…

Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other…

Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove…

We introduce a new notion of persistence modules endowed with operators. It encapsulates the additional structure on Floer-type persistence modules coming from the intersection product with classes in the ambient (quantum) homology, along…

In this paper, we extend the notion of directed clique complex to quivers and introduce an associated homology theory. By applying this construction to biquandle coloring quivers, we obtain new invariants of links. We then introduce a…