Related papers: Morse Cells

We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy…

We study the tropical version of the contraction morphism $\mathcal{T}$ between moduli spaces of stable and pseudostable curves. By promoting $\mathcal{T}$ to a logarithmic morphism, we obtain a piecewise linear function between the…

This paper is the third in a series that researches the Morse Theory, gradient flows, concavity and complexity on smooth compact manifolds with boundary. Employing the local analytic models from \cite{K2}, for \emph{traversally generic…

Fold maps are fundamental tools in the theory of singularities of differentiable maps and its applications to geometry. They are higher dimensional variants of Morse functions. Classes of special generic maps and round fold maps are…

This re-certifying paper describes the details of the Morse homology of manifolds with boundary, introduced by the author before, in terms of handlebody decompositions.

This paper begins the study of Morse theory for orbifolds, or more precisely for differentiable Deligne-Mumford stacks. The main result is an analogue of the Morse inequalities that relates the orbifold Betti numbers of an almost-complex…

A recent experimental realization of quantum degenerate gas of $^{40}$K$^{87}$Rb molecules opens up prospects of exploring strong dipolar Fermi gases and many-body phenomena arising in that regime. Here we derive a mean-field variational…

The question of paralleizability and stable parallelizability of a family of manifolds obtained as a quotients of circle action on the complex Stiefel manifolds are studied and settled.

The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2.…

We can approximate a continuous self-map $f$ of a compact metric space by discretizing the space into a grid. Through either the map itself or a time series, $f$ induces a multivalued grid map $\mathcal F$. The dynamical properties of…

As has been observed by Morse \cite{Mo}, any generic vector field $v$ on a compact smooth manifold $X$ with boundary gives rise to a stratification of the boundary $\d X$ by compact submanifolds $\{\d_j^\pm X(v)\}_{1 \leq j \leq \dim(X)}$,…

A smooth stably complex manifold is called a totally tangentially/normally split manifold (TTS/TNS-manifold, for short, resp.) if the respective complex tangential/normal vector bundle is stably isomorphic to a Whitney sum of complex linear…

Following recent results of A.K. and V.S. on $\mathbb Z$-graded manifolds, we give several local and global normal forms results for $Q$-structures on those, i.e. for differential graded manifolds. In particular, we explain in which sense…

We prove that the complement of a toric arrangement has the homotopy type of a minimal CW complex. As a corollary we obtain that the integer cohomology of these spaces is torsion free. We use Discrete Morse Theory, providing a sequence of…

For a finite simplicial complex K and a CW-pair (X,A), there is an associated CW-complex Z_K(X,A), known as a polyhedral product. We apply discrete Morse theory to a particular CW-structure on the n-sphere moment-angle complexes Z_K(D^{n},…

We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…

Let $M$ be a smooth manifold and let $\F$ be a codimension one, $C^\infty$ foliation on $M$, with isolated singularities of Morse type. The study and classification of pairs $(M,\F)$ is a challenging (and difficult) problem. In this…

Let $M$ be a smooth connected orientable compact surface. Denote by $F(M,S^1)$ the space of all Morse functions $f:M\to S^1$ having no critical points on the boundary of $M$ and such that for every boundary component $V$ of $M$ the…

Poisson structures vanishing linearly on a set of smooth closed disjoint curves are generic in the set of all Poisson structures on a compact connected oriented surface. We construct a complete set of invariants classifying these structures…

In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…