Burghelea, Dan
Overview
Works:  53 works in 144 publications in 5 languages and 1,966 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA387, 512.2 
Publication Timeline
.
Most widely held works by
Dan Burghelea
Groups of automorphisms of manifolds by
Dan Burghelea(
Book
)
26 editions published between 1974 and 2008 in English and German and held by 422 WorldCat member libraries worldwide
26 editions published between 1974 and 2008 in English and German and held by 422 WorldCat member libraries worldwide
The concordancehomotopy groups of geometric automorphism groups by
Peter L Antonelli(
Book
)
23 editions published between 1971 and 2008 in English and German and held by 421 WorldCat member libraries worldwide
23 editions published between 1971 and 2008 in English and German and held by 421 WorldCat member libraries worldwide
Variétés hilbertiennes; aspects géométriques by
Nicolaas H Kuiper(
Book
)
12 editions published between 1971 and 1973 in French and held by 207 WorldCat member libraries worldwide
12 editions published between 1971 and 1973 in French and held by 207 WorldCat member libraries worldwide
C*algebras and elliptic theory II by
Dan Burghelea(
Book
)
18 editions published in 2008 in English and Undetermined and held by 96 WorldCat member libraries worldwide
This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and noncommutative spaces. The topics covered include the index of operators, torsion invariants, Ktheory of operator algebras and L2invariants. The results presented in this book, which is largely inspired and stimulated by the AtiyahSinger index theorem, should be of interest to graduates and researchers in mathematical physics, differential topology and differential analysis
18 editions published in 2008 in English and Undetermined and held by 96 WorldCat member libraries worldwide
This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and noncommutative spaces. The topics covered include the index of operators, torsion invariants, Ktheory of operator algebras and L2invariants. The results presented in this book, which is largely inspired and stimulated by the AtiyahSinger index theorem, should be of interest to graduates and researchers in mathematical physics, differential topology and differential analysis
New topological invariants for real and anglevalued maps : an alternative to MorseNovikov theory by
Dan Burghelea(
Book
)
3 editions published in 2018 in English and held by 25 WorldCat member libraries worldwide
"This book is about new topological invariants of real and anglevalued maps inspired by Morse–Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics. They are the backbone of what the author proposes as a computational alternative to Morse–Novikov theory, referred to in this book as AMNtheory. These invariants are on one side analogues of rest points, instantons and closed trajectories of vector fields and on the other side, refine basic topological invariants like homology and monodromy. They are associated to tame maps, considerably more general than Morse maps, that are defined on spaces which are considerably more general than manifolds. They are computable by computer implementable algorithms and have strong robustness properties. They relate the dynamics of flows that admit the map as "Lyapunov map" to the topology of the underlying space, in a similar manner as Morse–Novikov theory does."Publisher's website
3 editions published in 2018 in English and held by 25 WorldCat member libraries worldwide
"This book is about new topological invariants of real and anglevalued maps inspired by Morse–Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics. They are the backbone of what the author proposes as a computational alternative to Morse–Novikov theory, referred to in this book as AMNtheory. These invariants are on one side analogues of rest points, instantons and closed trajectories of vector fields and on the other side, refine basic topological invariants like homology and monodromy. They are associated to tame maps, considerably more general than Morse maps, that are defined on spaces which are considerably more general than manifolds. They are computable by computer implementable algorithms and have strong robustness properties. They relate the dynamics of flows that admit the map as "Lyapunov map" to the topology of the underlying space, in a similar manner as Morse–Novikov theory does."Publisher's website
Introducere in topologia diferenṭialǎ(
Book
)
3 editions published in 1973 in Romanian and held by 7 WorldCat member libraries worldwide
3 editions published in 1973 in Romanian and held by 7 WorldCat member libraries worldwide
Hilbert manifolds by
Nicolaas H Kuiper(
Book
)
in English and held by 6 WorldCat member libraries worldwide
in English and held by 6 WorldCat member libraries worldwide
Acțiuni diferențiabile de grupuri Lie compacte by
Dan Burghelea(
Book
)
3 editions published in 1975 in 3 languages and held by 5 WorldCat member libraries worldwide
3 editions published in 1975 in 3 languages and held by 5 WorldCat member libraries worldwide
Power maps and epicyclic spaces by
Dan Burghelea(
Book
)
2 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
C*algebras and elliptic theory by
Bogdan Bojarski(
Book
)
1 edition published in 2006 in English and held by 4 WorldCat member libraries worldwide
Contains the proceedings of the conference on "C*algebras and Elliptic Theory" held in Bedlewo, Poland. This volume consists of papers and articles focussing on index theory and topology of manifolds, which offer a crosssection of significant advances in several fields, the main subject being Ktheory (of C*algebras, equivariant Ktheory)
1 edition published in 2006 in English and held by 4 WorldCat member libraries worldwide
Contains the proceedings of the conference on "C*algebras and Elliptic Theory" held in Bedlewo, Poland. This volume consists of papers and articles focussing on index theory and topology of manifolds, which offer a crosssection of significant advances in several fields, the main subject being Ktheory (of C*algebras, equivariant Ktheory)
A study of Fréchet manifolds by Palanivel Manoharan(
)
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
The first part of this thesis contains differential calculus of Frechet spaces. The Poincare lemma, the DeRham theorem and the equivariant DeRham theorem are verified. In an attempt to understand the space of maps or more generally the space of sections of fibre bundle among the class of Frechet manifolds, the second part contains the notion of deformation which is defined to be a triple $(E,K,p)$ where E and K are finite dimensional smooth manifolds and $p : E \to\ K$ is a submersion and the notion of ${\cal A}$manifolds. The main result establishes an equivalence between the category of deformations over K and a full subcategory of ${\cal A}$manifolds. This is a nonlinear version of Swan's theorem which states the equivalence between the category of smooth vector bundles over K and the category of finitely generated projective modules over ${\cal A}$ = $C\sp\infty(K)$
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
The first part of this thesis contains differential calculus of Frechet spaces. The Poincare lemma, the DeRham theorem and the equivariant DeRham theorem are verified. In an attempt to understand the space of maps or more generally the space of sections of fibre bundle among the class of Frechet manifolds, the second part contains the notion of deformation which is defined to be a triple $(E,K,p)$ where E and K are finite dimensional smooth manifolds and $p : E \to\ K$ is a submersion and the notion of ${\cal A}$manifolds. The main result establishes an equivalence between the category of deformations over K and a full subcategory of ${\cal A}$manifolds. This is a nonlinear version of Swan's theorem which states the equivalence between the category of smooth vector bundles over K and the category of finitely generated projective modules over ${\cal A}$ = $C\sp\infty(K)$
Elemente de analiza differenţiala calitativa : Pentru teoria catastrofelor elementare by
Dan Burghelea(
Book
)
3 editions published in 1977 in Romanian and Undetermined and held by 3 WorldCat member libraries worldwide
3 editions published in 1977 in Romanian and Undetermined and held by 3 WorldCat member libraries worldwide
New topological invariants for real and anglevalued maps : an alternative to MorseNovikov theory by
Dan Burghelea(
Book
)
1 edition published in 2018 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 3 WorldCat member libraries worldwide
Regularized determinants for pseudodifferential operators in vector bundles over S¹ by
Dan Burghelea(
Book
)
3 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
On the determinant of elliptic differential operators in vector bundles over S[beta] by
Dan Burghelea(
Book
)
3 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide
Euler structures, the variety of representations and the MilnorTuraev torsion by
Dan Burghelea(
Book
)
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
Topology of angle valued maps, bar codes and Jordan blocks by
Dan Burghelea(
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
In this paper one presents a collection of results relating the \bar codes" and \Jordan blocks", a new class of invariants for a tame angle valued map, with the topology of underlying space (and map). As a consequence one proposes refinements of Betti numbers and Novikov{Betti numbers provided by a continuous real or angle valued map defined on a compact ANR. These refinements can be interpreted as monic polynomials of degree the Betti numbers or Novikov{Betti numbers. One shows that these polynomials depend continuously on the real or the angle valued map and satisfy a Poincaré duality property in case the underlying space is a closed manifold. Our work offers an alternative perspective on Morse{Novikov theory which can be applied to a considerably larger class of spaces and maps and provides features inexistent in classical Morse{Novikov theory
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
In this paper one presents a collection of results relating the \bar codes" and \Jordan blocks", a new class of invariants for a tame angle valued map, with the topology of underlying space (and map). As a consequence one proposes refinements of Betti numbers and Novikov{Betti numbers provided by a continuous real or angle valued map defined on a compact ANR. These refinements can be interpreted as monic polynomials of degree the Betti numbers or Novikov{Betti numbers. One shows that these polynomials depend continuously on the real or the angle valued map and satisfy a Poincaré duality property in case the underlying space is a closed manifold. Our work offers an alternative perspective on Morse{Novikov theory which can be applied to a considerably larger class of spaces and maps and provides features inexistent in classical Morse{Novikov theory
Diffeomorphisms for Hilbert manifolds and handle decomposition by
Dan Burghelea(
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
The geometric complex of a MorseBottsmale pair and an extension of a theorem by BismutZhang by
Dan Burghelea(
Book
)
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
Imbedding Hilbert manifolds with given normal bundle by
Dan Burghelea(
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
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