Eta Invariant and Conformal Cobordism
نویسنده
چکیده
In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an Abelian group, the conformal cobordism group, which classifies the conformally flat structures according to whether they bound conformally flat structures in a conformally invariant way. The eta invariant gives rise to a homomorphism from this group to the circle group, which can be highly nontrivial. It remains an interesting question of how to compute this group. Mathematics Subject Classification (2000): 55N22.
منابع مشابه
Conformally Flat Structures and Hyperbolic Structures
We define an abelian group, the conformal cobordism group of hyperbolic structures, which classifies the hyperbolic structures according to whether it bounds a (higher dimensional) conformally flat structure in a conformally invariant way. We then construct a homomorphism from this group to the circle group, using the eta invariant. The homomorphism can be highly nontrivial. It remains an inter...
متن کاملBoundaries, Eta Invariant and the Determinant Bundle
Cobordism invariance shows that the index, in K-theory, of a family of pseudodifferential operators on the boundary of a fibration vanishes if the symbol family extends to be elliptic across the whole fibration. For Dirac operators with spectral boundary condition, Dai and Freed [5] gave an explicit version of this at the level of the determinant bundle. Their result, that the eta invariant of ...
متن کاملm at h . D G ] 1 4 Se p 20 07 Boundaries , eta invariant and the determinant bundle
Cobordism invariance shows that the index, in K-theory, of a family of pseudodifferential operators on the boundary of a fibration vanishes if the symbol family extends to be elliptic across the whole fibration. For Dirac operators with spectral boundary condition, Dai and Freed [5] gave an explicit version of this at the level of the determinant bundle. Their result, that the eta invariant of ...
متن کاملنظریه میدان اسکالر کلاسیک با تقارن همدیس و پتانسیل نامثبت
We review the conformal symmetry group and investigate the isomorphism between the conformal group and O( D,2 ) . We study the classically conformal invariant scalar theory in D -dimensions with a non-positive potential . We solve the equations of motion by assigning O(D-1, 2)symmetry to the classical solutions with broken translational symmetry in all directions. Then we consider a six d...
متن کاملOn the cobordism and commutative monoid with cancellation approaches to conformal field theory
In the late 1980s, Graeme Segal axiomatized conformal field theory in terms of a cobordism category. In that same preprint he outlined a more symmetric trace approach, which was recently rigorized in terms of pseudo algebras over a 2-theory. In this paper, we treat the cobordism approach in the pseudo algebra context. We introduce a new algebraic structure on a bicategory, called a pseudo 2-alg...
متن کامل