49 citations · 216 across the 41 of their papers we have counts for
41 papers
"Barcodes" for continuous maps and a brief introduction to Alternative Morse Theory
Dan Burghelea
This paper reviews the description of "bar codes" for a continuous real-valued map and explains how to recover the Morse complex of a Morse function from them. In this presentation…
Note on the conjugacy classes of elements and their centralizers for the free product of two groups
Dan Burghelea
We describe the conjugacy classes of the elements of the free product of two groups and their centralizers and, as a consequence, we correct the calculation of the cyclic and perio…
Alternative to Morse-Novikov Theory for a closed 1-form (II)
Dan Burghelea
This paper is a continuation of Alternative to Morse-Novikov Theory for a closed 1-form(I), and establishes: a) a refinement of Poincaré duality to an equality between the configur…
Virtually small spectral package of a Riemannian manifold
Dan Burghelea, Yoonweon Lee
For a Morse function on a closed orientable Riemannian manifold one introduces the {\it virtually small spectral package} an analytic object consisting of a finite number of analyt…
Witten deformation and the spectral package of a Riemannian manifold
Dan Burghelea
The Witten deformation associated to a Morse function on a closed Riemannian manifold, via Rellich-Kato theorem, relates analytically the spectral package of the Riemannian manifol…
Comparison between "Parametrized homology via zigzag persistence" and "Refined homology in the presence of a real-valued continuous function"
Dan Burghelea
In this note one shows that the four persistence diagrams and measures defined in [5] are particular cases of the maps and the measures discussed in [2] and [1]