Differential characters and geometric invariants

  title={Differential characters and geometric invariants},
  author={Jeff Cheeger and James Simons},
This paper first appeared in a collection of lecture notes which were distributed at the A.M.S. Summer Institute on Differential Geometry, held at Stanford in 1973. Since then it has been (and remains) the authors' intention to make available a more detailed version. But, in the mean time, we continued to receive requests for the original notes. Moreover, the secondary invariants we discussed have recently arisen in some new contexts, e.g. in physics and in the work of Cheeger and Gromov on… Expand
From Sparks to Grundles--Differential Characters
We introduce a new homological machine for the study of secondary geometric invariants. The objects, called spark complexes, occur in many areas of mathematics. The theory is applied here toExpand
Differential Characters for K-theory
We describe a sequence of results that begins with the introduction of differential characters on singular cycles in the seventies motivated by the search for invariants of geometry or more generallyExpand
Torsion in Cohomology Groups of Configuration Spaces
An important and surprising discovery in physics in the last fifty years is that if quantum particles are constrained to move in two rather than three dimensions, they can in principle exhibit newExpand
Degeneration of Riemannian metrics under Ricci curvature bounds
These notes are based on the Fermi Lectures delivered at the Scuola Normale Superiore, Pisa, in June 2001. The principal aim of the lectures was to present the structure theory developed by TobyExpand
A topological proof of Bloch's conjecture
The following is an outline of the structure of the thesis. • In the first chapter, after reviewing the Chern Weil construction of characteristic classes of bundles I introduce the constructionsExpand
Uniqueness of differential characters and differential K-theory via homological algebra
  • Ishan Mata
  • Mathematics
  • Journal of Homotopy and Related Structures
  • 2020
In Proc Math Sci 129, 70(219), Rakesh Pawar considers and solves a certain extension problem. In this note, we observe that the existence and uniqueness of differential characters (defined as objectsExpand
This paper introduces a general method for relating characteristic classes to singu-larities of a bundle map. The method is based on the notion of geometric atomicity. This is a property of bundleExpand
Homologie cyclique et K-théorie
This book is an expanded version of some ideas related to the general problem of characteristic classes in the framework of Chern-Weil theory. These ideas took their origins independtly from the workExpand
Lectures on Cohomology, T-Duality, and Generalized Geometry
These are notes for lectures, originally entitled “Selected Mathematical Aspects of Modern Quantum Field Theory”, presented at the Summer School “New Paths Towards Quantum Gravity”, Holbae k,Expand
Perspectives on geometric analysis
This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion ofExpand


Introduction. The object of this paper is to prove Theorem 2 of §2, which shows, for any connexion, how the curvature form generates the holonomy group. We believe this is an extension of a theoremExpand
A remark on the integral cohomology of BΓq
In this paper we provide a negative answer to the question raised in [l] as to whether these results hold over the integers. We do this by constructing enough examples of foliations whose integralExpand
Spectral Asymmetry and Riemannian Geometry
This has an analytic continuation to the whole s-plane as a meromorphic function of 5 and s = 0 is not a pole: moreover CA(o) can be computed as an explicit integral over the manifold [9]. In thisExpand
Extensions and low dimensional cohomology theory of locally compact groups. II
Introduction. In a previous paper [8], we have defined a sequence of cohomology groups Hr(G, A) defined when G is a locally compact group and A is an abelian locally compact group on which G actsExpand
Characters and cohomology of finite groups
© Publications mathématiques de l’I.H.É.S., 1961, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
On a topological obstruction to integrability,
  • Proc. Internat. Congress Math. (Nice
  • 1970