A Cyclic Cocycle and Relative Index Theorems on Partitioned Manifolds
نویسندگان
چکیده
منابع مشابه
Index Theorems and Magnetic Monopoles on Asymptotically Conic Manifolds
In this thesis, I investigate the index of Callias type operators on asymptotically conic manifolds (also known as asymptotically locally Euclidean manifolds or scattering manifolds) and give an application to the moduli space of magnetic monopoles on these spaces. The index theorem originally due to C. Callias and later generalized by N. Anghel and others concerns operators of the form D + it,...
متن کاملRelative Zeta Functions, Determinants, Torsion, Index Theorems and Invariants for Open Manifolds
The set of Clifford bundles of bounded geometry over open manifolds can be endowed with a metrizable uniform structure. For one fixed bundle E we define the generalized component gen comp(E) as the set of Clifford bundles E′ which have finite distance to E. If D, D′ are the associated generalized Dirac operators, we prove for the pair (D,D′) relative index theorems, define relative ζ– and η– fu...
متن کاملSpinors on manifolds with boundary: APS index theorems with torsion
Index theorems for the Dirac operator allow one to study spinors on manifolds with boundary and torsion. We analyse the modifications of the boundary Chern–Simons correction and APS η invariant in the presence of torsion. The bulk contribution must also be modified and is computed using a supersymmetric quantum mechanics representation. Here we find agreement with existing results which employe...
متن کاملVanishing theorems on Hermitian manifolds
We prove the vanishing of the Dolbeault cohomology groups on Hermitian manifolds with ddc-harmonic Kähler form and positive (1, 1)-part of the Ricci form of the Bismut connection. This implies the vanishing of the Dolbeault cohomology groups on complex surfaces which admit a conformal class of Hermitian metrics, such that the Ricci tensor of the canonical Weyl structure is positive. As a coroll...
متن کاملVanishing Theorems on Covering Manifolds
Let M be an oriented even-dimensional Riemannian manifold on which a discrete group Γ of orientation-preserving isometries acts freely, so that the quotientX = M/Γ is compact. We prove a vanishing theorem for a half-kernel of a Γ-invariant Dirac operator on a Γ-equivariant Clifford module overM , twisted by a sufficiently large power of a Γ-equivariant line bundle, whose curvature is non-degene...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 2019
ISSN: 0387-3870
DOI: 10.3836/tjm/1502179288