An integral formula for non-Codazzi tensors
An integral formula for submanifolds and its application
An integral formula for Willmore surfaces in an -dimensional sphere.
An integral formula in differential geometry via mixed exterior algebra.
An integral formula related to inner isoptics
An integral geometry problem along geodesics and a computational approach.
An integral geometry problem in a nonconvex domain.
An intrinsic characterization of Kähler manifolds.
An intrinsic definition of the Dirac operator.
An introduction to algebraic K-theory
This paper gives an exposition of algebraic K-theory, which studies functors , an integer. Classically introduced by Bass in the mid 60’s (based on ideas of Grothendieck and others) and introduced by Milnor [Introduction to algebraic K-theory, Annals of Math. Studies, 72, Princeton University Press, 1971: Zbl 0237.18005]. These functors are defined and applications to topological K-theory (Swan), number theory, topology and geometry (the Wall finiteness obstruction to a CW-complex being finite,...
An introduction to Cartan Geometries
A principal bundle with a Lie group consists of a manifold and a free proper smooth -action . There is a unique smooth manifold structure on the quotient space such that the canonical map is smooth. is called a base manifold and stands for the bundle. The most fundamental examples of principal bundles are the homogeneous spaces , where is a closed subgroup of . The pair is a Klein pair. A model geometry consists of a Klein pair and a Lie group with Lie algebra . In this...
An introduction to gerbes on orbifolds
This paper is a gentle introduction to some recent results involving the theory of gerbes over orbifolds for topologists, geometers and physicists. We introduce gerbes on manifolds, orbifolds, the Dixmier-Douady class, Beilinson-Deligne orbifold cohomology, Cheeger-Simons orbifold cohomology and string connections.
An introduction to quantum sheaf cohomology
In this note we review “quantum sheaf cohomology,” a deformation of sheaf cohomology that arises in a fashion closely akin to (and sometimes generalizing) ordinary quantum cohomology. Quantum sheaf cohomology arises in the study of (0,2) mirror symmetry, which we review. We then review standard topological field theories and the A/2, B/2 models, in which quantum sheaf cohomology arises, and outline basic definitions and computations. We then discuss (2,2) and (0,2) supersymmetric Landau-Ginzburg...
An introduction to spectral and differential geometry in Carnot-Carathéodory spaces
An introduction to spherical orbit spaces.
An introduction to symplectic topology
An introduction to the completeness of compact semi-riemannian manifolds
An introduction to the Einstein-Vlasov system
An invariant of nonpositively curved contact manifolds
We define an invariant of contact structures and foliations (on Riemannian manifolds of nonpositive sectional curvature) which is upper semi-continuous with respect to deformations and thus gives an obstruction to the topology of foliations which can be approximated by isotopies of a given contact structure.
An isoembolic pinching theorem.