Related papers: Discrete Morse-Bott theory for CW complexes
A short proof of convergence for the discretization of the Hodge-Dirac operator in the framework of discrete exterior calculus (DEC) is provided using the techniques established in [Johnny Guzm\'an and Pratyush Potu, A Framework for…
We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type…
Moderate deviations for random complex zeroes are deduced from a new theorem on moderate deviations for random fields.
In this paper, we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the unit cube due to Roth holds true also for a suitable finite…
Banyaga and Hurtubise defined the Morse-Bott-Smale chain complex as a quotient of a large chain complex by introducing five degeneracy relations. However, their five degeneracy relations are in fact redundant. In the present paper, we unify…
In this paper we introduce Morse Lie groupoid morphisms and study their main properties. We show that this notion is Morita invariant which gives rise to a well defined notion of Morse function on differentiable stacks. We show a groupoid…
We discuss the cone and contraction theorem in a suitable complex analytic setting. More precisely, we establish the cone and contraction theorem of normal pairs for projective morphisms between complex analytic spaces. This result is a…
We survey recent results about the Torelli question for holomorphic-symplectic varieties. Following are the main topics. A Hodge theoretic Torelli theorem. A study of the subgroup W, of the isometry group of the weight 2 Hodge structure,…
As a topic of mathematics, "arrangements", systems of hyperplanes, circles, and general (regular) submanifolds, attract us strongly. We present a natural elementary study of arrangements of circles. It is also a kind of new studies. Our…
In this paper, we apply Conley index theory in a covering space of an invariant set $S$, possibly not isolated, in order to describe the dynamics in $S$. More specifically, we consider the action of the covering translation group in order…
Along with excursions into manifolds with corners, resolution towers of Thom and Whitney stratifications, I show that for a generic gradientlike vector field on a manifold with a Morse function, the stable manifolds give a CW decomposition…
Given a CW-complex A we define an `A-shaped' homology theory which behaves nicely towards A-homotopy groups allowing the generalization of many classical results. We also develop a relative version of the Federer spectral sequence for…
Geometric discretisation draws analogies between discrete objects and operations on a complex with continuum ones on a manifold. We generalise the theory to the cubic case and incorporate metric, by adding volume factors to our discrete…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
On a smooth manifold, we associate to any closed differential form a mapping cone complex. The cohomology of this mapping cone complex can vary with the de Rham cohomology class of the closed form. We present a novel Morse theoretical…
We introduce the notion of mixed Hodge complex on an algebraic variety, improving Du Bois' filtered complex, and relate Deligne's theory of mixed Hodge structure with the theory of mixed Hodge module. This was supposed to be true, but is…
This paper proves some results on negative gradient dynamics of Morse functions on Hilbert manifolds. It contains the compactness of flow lines, manifold structures of certain compacti- fied moduli spaces, orientation formulas, and CW…
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…
Conley index theory is a very powerful tool in the study of dynamical systems, differential equations and bifurcation theory. In this paper, we make an attempt to generalize the Conley index to discrete random dynamical systems. And we…
We discuss some variants of cone theorem for movable curves in any codimensions.