To a polynomial function $f$ with arbitrary singularities we associate the number of Morse points in a general linear Morsification $f_{t} := f - t\ell$. We produce computable algebraic formulas in terms of invariants of $f$ for the numbers of stratwise Morse trajectories which abut, as $t\to 0$, to some point of $X$ or to some point at infinity.Comment: 16
We consider the problem of counting the number of varieties in a family over $\mathbb{Q}$ with a rat...
We define a class of multiparameter persistence modules that arise from a one-parameter family of fu...
Elaborating on work by Abouzaid and Mescher, we prove that the Morse cochain complex of a Morse func...
To a polynomial function $f$ with arbitrary singularities we associate the number of Morse points in...
An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical predi...
An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical predi...
An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical predi...
International audienceThe algorithm for calculation of "canonical form" = "persistence barcodes/diag...
Morse theory is an extremely versatile tool, useful in a variety of situations and parts of topology...
Étant donnée une fonction de Morse sur une variété fermée orientée, nous nous inspirons de travaux d...
AbstractWe describe how to compute topological objects associated to a polynomial map of several com...
In this paper, we define the homological Morse numbers of a filtered cell complex in terms of the re...
There is canonical partition of set of critical values of smooth function into pairs "birth-death" a...
Mathematicians have long been interested in studying the properties of simplicial complexes. In 1998...
I am working on several topics in number theory, arithmetic geometry and arithmetic dynamics. One to...
We consider the problem of counting the number of varieties in a family over $\mathbb{Q}$ with a rat...
We define a class of multiparameter persistence modules that arise from a one-parameter family of fu...
Elaborating on work by Abouzaid and Mescher, we prove that the Morse cochain complex of a Morse func...
To a polynomial function $f$ with arbitrary singularities we associate the number of Morse points in...
An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical predi...
An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical predi...
An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical predi...
International audienceThe algorithm for calculation of "canonical form" = "persistence barcodes/diag...
Morse theory is an extremely versatile tool, useful in a variety of situations and parts of topology...
Étant donnée une fonction de Morse sur une variété fermée orientée, nous nous inspirons de travaux d...
AbstractWe describe how to compute topological objects associated to a polynomial map of several com...
In this paper, we define the homological Morse numbers of a filtered cell complex in terms of the re...
There is canonical partition of set of critical values of smooth function into pairs "birth-death" a...
Mathematicians have long been interested in studying the properties of simplicial complexes. In 1998...
I am working on several topics in number theory, arithmetic geometry and arithmetic dynamics. One to...
We consider the problem of counting the number of varieties in a family over $\mathbb{Q}$ with a rat...
We define a class of multiparameter persistence modules that arise from a one-parameter family of fu...
Elaborating on work by Abouzaid and Mescher, we prove that the Morse cochain complex of a Morse func...