Weiping Zhang
Eta invariant and holonomy, the even dimensional case.
Fri, 05/04/2012 - 15:01 — SomNambulAuthors: Weiping Zhang, Xianzhe Dai
Subjects: Differential Geometry
AbstractIn previous work, we introduced eta invariants for even dimensional
manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer,
which is for odd dimensional manifolds. It is associated to $K^1$
representatives on even dimensional manifolds and is closely related to the so
called WZW theory in physics. In fact, it is an intrinsic interpretation of the
Wess-Zumino term without passing to the bounding 3-manifold.Hopf cyclic cohomology and Hodge theory for proper actions.
Wed, 02/24/2010 - 16:01 — SomNambulAuthors: Weiping Zhang, Xiang Tang, Yi-jun Yao
Subjects: Differential Geometry
AbstractWe introduce a Hopf algebroid associated to a proper Lie group action on a
smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is
equal to the de Rham cohomology of invariant differential forms. When the
action is cocompact, we develop a generalized Hodge theory for the de Rham
cohomology of invariant differential forms. We prove that every cyclic
cohomology class of the Hopf algebroid is represented by a generalized harmonic
form. This implies that the space of cyclic cohomology of the Hopf algebroid is
finite dimensional.A Poincar\'e-Hopf type formula for Chern character numbers.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Huitao Feng, Weiping Li, Weiping Zhang
Subjects: Geometric Topology
AbstractFor two complex vector bundles admitting a homomorphism with isolated
singularities between them, we establish a Poincar\'e-Hopf type formula for the
difference of the Chern character numbers of these two vector bundles. As a
consequence, we extend the original Poincar\'e-Hopf index formula to the case
of complex vector fields.
User login
