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Higher index theory for certain expanders and Gromov monster groups II
Higher index theory certain expanders Gromov monster groups II
2011/2/22
In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse B...
Higher index theory for certain expanders and Gromov monster groups I
Higher index theory certain expanders Gromov monster groups I
2011/2/22
In this paper, the first of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs is an expander and the girth of the graphs tends to infin...
In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various ...
We study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian mani...
On the finiteness of the Morse Index for Schrödinger operators
the Morse Index Schrö dinger operators
2010/11/19
Let H=$\Delta +V$ be a Schr\"odinger on a complete non-compact manifold. It is known since the work of Fischer-Colbrie and Schoen that the finiteness of the negative spectrum of $H$ implies the exist...
Let $\mathfrak a$ be an algebraic Lie subalgebra of a simple Lie algebra $\mathfrak g$ with index $\mathfrak a \leq \rank \mathfrak g$. Let $Y(\mathfrak a)$ denote the algebra of $\mathfrak a$ invari...
The Connes-Chern Character and The Atiyah-Patodi-Singer Index Theorem for Odd Dimensional Manifolds with Boundary
The Connes-Chern Character The Atiyah-Patodi-Singer Index Theorem
2010/11/9
We prove an analogue for odd dimensional manifolds with boundary, in the $b$-calculus setting, of the higher Atiyah-Patodi-Singer index theorem by Getzler and by Wu.
Signs in the cd-index of Eulerian partially ordered sets
the cd-index Eulerian partially ordered sets
2010/10/29
A graded partially ordered set is Eulerian if every interval has the same number of elements of even rank and of odd rank. Face lattices of convex polytopes are Eulerian. For Eulerian partially order...