49 citations · 216 across the 41 of their papers we have counts for
17 papers · 1 filter
"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…
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…
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]
Alternative to Morse-Novikov Theory for closed 1-form (I)
Dan Burghelea
This paper extends the Alternative to Morse-Novikov theory we have proposed in Burghelea (New topological invariants for real- and angle valued maps, World Scientific, Hackensack,…
Barcodes for closed one form - an alternative to Novikov theory
Dan Burghelea
We extend the configurations discussed in Burghelea's book and Burghelea-Haller's paper on topology of angle-valued maps, equivalently the closed, open and closed-open bar codes fr…
Barcodes in level and sub level persistence and Morse-Novikov theory
Dan Burghelea
In this note we recall the relations between the barcodes in level and sub-level persistence and make precise their relation with the Morse-Novikov complex of a Morse real- or angl…
New invariants for a real valued and angle valued map (an Alternative to Morse- Novikov theory)
Dan Burghelea
This paper but section 6 is essentially my lecture at The Eighth Congress of Romanian Mathematicians, June 26 - July 1, 2015, Iasi, Romania. The paper summarizes the definitions an…
A refinement of Betti numbers and homology in the presence of a continuous function II (the case of an angle valued map)
Dan Burghelea
For a continuous angle-valued map defined on a compact ANR, a fixed field and any degree one proposes a refinement of the Novikov-Betti number and of the Novikov homology of the pa…
Refinement of Novikov - Betti numbers and of Novikov homology provided by an angle valued map
Dan Burghelea
To a pair (X,f), X compact ANR and f a continuous angle valued map defined on X, a fixed field and a nonnegative integer one assigns a finite configuration of complex numbers with…
Linear relations, monodromy and Jordan cells of a circle valued map
Dan Burghelea
In this paper we consider the definition of " monodromy of an angle valued map" based on linear relations as proposed in Burghelea-Haller (3). This definition provides an alternati…
A refinement of Betti numbers in the presence of a continuous function. ( I )
Dan Burghelea
We propose a refinement of the Betti numbers and of the homology with coefficients in a field of a compact ANR in the presence of a continuous real valued function. The refinement…
Topology of angle valued maps, bar codes and Jordan blocks
Dan Burghelea, Stefan Haller
In this paper one presents a collection of results about the "bar codes" and "Jordan blocks" introduced by Burghelea-Day as "computer friendly" invariants of a tame angle-valued ma…
Topology Of Real And Angle Valued Maps And Graph Representations (A Brief Survey)
Dan Burghelea
(lecture delivered at the Congress of the Romanian mathematicians, Brasov, June 2011) Using graph representations a new class of computable topological invariants associated with a…
Graph Representations and Topology of Real and Angle Valued Maps
Dan Burghelea, Stefan Haller
In this paper we review the definition of the invariants "bar codes" and "Jordan cells" of real and angle valued tame maps as proposed in Burghelea and Dey and Carlsson et al and p…
Persistence for Circle Valued Maps
Dan Burghelea, Tamal K. Dey
We study circle valued maps and consider the persistence of the homology of their fibers. The outcome is a finite collection of computable invariants which answer the basic questio…
Defining and Computing Topological Persistence for 1-cocycles
Dan Burghelea, Tamal K. Dey, Du Dong
The concept of topological persistence, introduced recently in computational topology, finds applications in studying a map in relation to the topology of its domain. Since its int…
Cyclic theory for commutative differential graded algebras and s-cohomology
Dan Burghelea
In this paper one considers three homotopy functors on the category of manifolds, and parallel them with other three homotopy functors on the category…