Related papers: On an index theorem by Bismut
This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.
By a re-examination of MacMahon's original proof of his celebrated theorem on the distribution of the major indices over permutations, we give a reformulation of his argument in terms of the structure of labeled partitions. In this…
We prove a duality theorem for graded algebras over a field that implies several known duality results : graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and…
For the generalized oscillator, we prove a Rellich type theorem, or characterize the order of growth of eigenfunctions. The proofs are given by an extensive use of commutator arguments invented recently by Ito and Skibsted. These arguments…
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We present an elementary proof of the cross theorem in the case of Reinhardt domains. The results illustrates the well-known interrelations between the holomorphic geometry of a Reinhardt domain and the convex geometry of its logarithmic…
We present an index theorem for certain hypoelliptic differential operators on foliated manifolds. Our proof is a development of Alain Connes tangent groupoid proof of the Atiyah-Singer index theorem. The paper is largely self-contained.
We prove an identity about partitions, previously conjectured in the study of shifted Jack polynomials (math.CO/9903020). The proof given is using $\lambda$-ring techniques. It would be interesting to obtain a bijective proof.
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.
We prove Lipshitz's Maslov index formula in Heegaard Floer homology via the combinatorics of Heegaard diagrams.
We prove a Givental-style mirror theorem for toric Deligne--Mumford stacks X. This determines the genus-zero Gromov--Witten invariants of X in terms of an explicit hypergeometric function, called the I-function, that takes values in the…
Recently, two of the authors of this paper constructed cyclic cocycles on Harish-Chandra's Schwartz algebra of linear reductive Lie groups that detect all information in the $K$-theory of the corresponding group $C^*$-algebra. The main…
In this note, we give a short proof of the Torelli theorem for cubic fourfolds that relies on the global Torelli theorem for irreducible holomorphic symplectic varieties proved by Verbitsky.
A resonance theorem providing existence of functions that are counterexamples for all members of a given family of translation invariant differentiation bases is proved. Applications of the theorem to Zygmund problem on a choice of…
We give a new proof of a theorem of B.M. Bredihin which was originally proved by extending Linnik's solution, via his dispersion method, of a problem of Hardy and Littlewood.
In this paper an analytic proof of a generalization of a theorem of Bismut ([Bis1, Theorem 5.1]) is given, which says that, when $v$ is a transversal holomorphic vector field on a compact complex manifold $X$ with a zero point set $Y$, the…
The computation of the index of the Hessian of the action functional in semi-Riemannian geometry at geodesics with two variable endpoints is reduced to the case of a fixed final endpoint. Using this observation, we give an elementary proof…
This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.
In this paper we study an analogue of the classical Riemann-Hilbert problem stated for the classes of difference and $q$-difference systems. The Birkhoff's existence theorem was generalized in this paper.
We reformulate, in the context of continuous logic, an oscillation theorem originally proved by G. Hjorth. We give a proof of the theorem in that setting which is similar to, but simpler than, Hjorth's original one. The point of view…