منابع مشابه
Superconnections and Higher Index Theory
Let M be a smooth closed spin manifold. The higher index theorem computes the pairing between the group cohomology of π1(M) and the Chern character of the “higher” index of a Dirac-type operator on M. Using superconnections, we give a heat equation proof of this theorem on the level of differential forms on a noncommutative base space. As a consequence, we obtain a new proof of the Novikov conj...
متن کاملNoncommutative Geometric Gauge Theory from Superconnections
Noncommutative geometric gauge theory is reconstructed based on the superconnection concept. The bosonic action of the Connes-Lott model including the symmetry breaking Higgs sector is obtained by using a new generalized derivative, which consists of the usual 1-form exterior derivative plus an extra element called the matrix derivative, for the curvatures. We first derive the matrix derivative...
متن کاملRandom graphs, weak coarse embeddings, and higher index theory
This paper studies higher index theory for a random sequence of bounded degree, finite graphs with diameter tending to infinity. We show that in a natural model for such random sequences the following hold almost surely: the coarse Baum-Connes assembly map is injective; the coarse Baum-Connes assembly map is not surjective; the maximal coarse BaumConnes assembly map is an isomorphism. These res...
متن کاملOn the Higher Randić Index
Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih v v v over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher R...
متن کاملITERATED INTEGRALS OF SUPERCONNECTIONS 0902a
Iterated integration of a connection gives the holonomy or parallel transport of the connection. Iterated integration of a superconnection gives something else which we call a “superconnection parallel transport.” We ask under what conditions are the holonomies of a connection on a graded vector bundle chain maps and under what conditions the superconnection parallel transports give homotopies ...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 1992
ISSN: 1016-443X,1420-8970
DOI: 10.1007/bf01896662