The mathematical work of V. K. Patodi

DOI10.1007/s40304-014-0039-5zbMath1316.58020arXiv1502.03637OpenAlexW2135149597MaRDI QIDQ2341080

Publication date: 22 April 2015

Published in: Communications in Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.03637

zbMATH Keywords

survey analytic torsion $\eta$ invariant local index Patodi

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Eta-invariants, Chern-Simons invariants (58J28) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Cites Work

Loop Spaces and the hypoelliptic Laplacian
Riemann-Roch theorems for differentiable manifolds
The index of elliptic operators on compact manifolds
Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
Supersymmetry and the Atiyah-Singer index theorem
Higher spectral flow
An anomaly formula for Ray-Singer metrics on manifolds with boundary
Real embeddings and the Atiyah-Patodi-Singer index theorem for Dirac operators
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Eta invariants, signature defects of cusps, and values of L-functions
The Atiyah-Singer theorems: A probabilistic approach. I: The index theorem
Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
Families index for manifolds with boundary, superconnections, and cones. I: Families of manifolds with boundary and Dirac operators
Families index for manifolds with boundary, superconnections and cones. II: The Chern character
An index theorem in differential $K$-theory
Superconnections and the Chern character
Signature defects of cusps of Hilbert modular varieties and values of L- series at $s=1$
Global gravitational anomalies
The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
Localization formulas, superconnections, and the index theorem for families
Determinants of Cauchy-Riemann operators on a Riemann surface
A short proof of the local Atiyah-Singer index theorem
$\eta$-invariants, the adiabatic approximation and conical singularities
The logarithm of the Dedekind $\eta$-function
The analysis of elliptic families. I: Metrics and connections on determinant bundles
The analysis of elliptic families. II: Dirac operators, êta invariants, and the holonomy theorem
Quantum field theory and the Jones polynomial
Local index theory and higher analytic torsion
Supersymmetry and Morse theory
On the variation in the cohomology of the symplectic form of the reduced phase space
Adiabatic limits of the $\eta$-invariants. The odd-dimensional Atiyah- Patodi-Singer problem
Perturbative expansion of Chern-Simons theory with non-compact Gauge group
Spectrum and the fixed point sets of isometries. II
Analytic torsion and R-torsion of Riemannian manifolds
Analytic torsion and the heat equation
Real embeddings and eta invariants
On the index of geometrical operators for Riemannian manifolds with boundary
Circle bundles, adiabatic limits of $\eta$-invariants and Rokhlin congruences
Eta invariants and manifolds with boundary
Families of Dirac operators, boundaries and the $B$-calculus
Dirac index classes and the noncommutative spectral flow
Elliptic operators and higher signatures.
$\eta$-invariant and Chern-Simons current
Homotopieringe und Linsenräume
Characteristic forms and geometric invariants
Hilbert modular surfaces
On the gluing problem for the $\eta$-invariant
$\mathbb{R} /\mathbb{Z}$ index theory
Hypoelliptic Laplacian and Bott-Chern cohomology. A theorem of Riemann-Roch-Grothendieck in complex geometry
On the gluing formula for the analytic torsion
Real embeddings, $\eta$-invariant and Chern-Simons current
The hypoelliptic Laplacian, analytic torsion and Cheeger-Müller theorem
Eta-invariants, torsion forms and flat vector bundles
An index theorem for Toeplitz operators on odd-dimensional manifolds with boundary
A Lefschetz fixed point formula for elliptic complexes. I
The index of elliptic operators. I
The index of elliptic operators. II
The index of elliptic operators. III
A Lefschetz fixed point formula for elliptic complexes. II: Applications
Curvature and the eigenvalues of the Laplacian
Curvature and the eigenforms of the Laplace operator
The index of elliptic operators. IV, V
An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds
R-torsion and the Laplacian on Riemannian manifolds
On the heat equation and the index theorem
Curvature and the eigenvalues of the Laplacian for the Dolbeault complex
Curvature and the eigenvalues of the Laplacian for elliptic complexes
Analytic torsion for complex manifolds
A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds
Computations and Applications of η Invariants
Index Theory and the Hypoelliptic Laplacian
Adiabatic limit, Bismut-Freed connection, and the real analytic torsion form
Hypoelliptic Laplacian and Orbital Integrals (AM-177)
Spectral Asymmetry and Riemannian Geometry
The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167)
Torsion Invariants for Families
A computation of the equivariant index of the Dirac operator
Local index theorem for Dirac operator
η-Invariants and Their Adiabatic Limits
Adiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence
A Direct Geometric Proof of the Lefschetz Fixed Point Formulas
Transgressed Euler classes of ${\rm SL}(2n,\mathbf{Z})$ vector bundles, adiabatic limits of eta invariants and special values of $L$-functions
Spectral asymmetry and Riemannian Geometry. I
Spectral asymmetry and Riemannian geometry. II
Finite-Difference Approach to the Hodge Theory of Harmonic Forms
Spectral asymmetry and Riemannian geometry. III
η-invariants and determinant lines
The hypoelliptic Laplacian on the cotangent bundle
The [eta-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary]
Holomorphic Lefschetz fixed point formula
Flat Vector Bundles, Direct Images and Higher Real Analytic Torsion
Circle Bundles and the Kreck-Stolz Invariant
Analytic Torsion and R-Torsion for Unimodular Representations

This page was built for publication: The mathematical work of V. K. Patodi