The Equivariant Coarse Novikov Conjecture and Coarse Embedding

2 8 Ju l 2 00 5 The coarse geometric Novikov conjecture and uniform convexity

The classic Atiyah-Singer index theory of elliptic operators on compact manifolds has been vastly generalized to higher index theories of elliptic operators on noncompact spaces in the framework of noncommutative geometry [5] by Connes-Moscovici for covering spaces [8], Baum-Connes for spaces with proper and cocompact discrete group actions [2], Connes-Skandalis for foliated manifolds [9], and ...

The Coarse Baum – Connes Conjecture for Spaces Which Admit a Uniform Embedding into Hilbert Space

The coarse Baum–Connes conjecture and groupoids. II

Given a (not necessarily discrete) proper metric space M with bounded geometry, we define a groupoid G(M). We show that the coarse Baum–Connes conjecture with coefficients, which states that the assembly map with coefficients for G(M) is an isomorphism, is hereditary by taking closed subspaces.

Coarse-graining of bubbling geometries and the fuzzball conjecture

In the LLM bubbling geometries, we compute the entropies of black holes and estimate their “horizon” sizes from the fuzzball conjecture, based on coarse-graining on the gravity side. The differences of black hole microstates cannot be seen by classical observations. Conversely, by counting the possible deformations of the geometry which are not classically detectable, we can calculate the entro...

Institute for Advanced Simulation DFT Embedding and Coarse Graining Techniques

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