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Curved noncommutative torus and Gauss--Bonnet
noncommutative torus Gauss--Bonnet Quantum Algebra
2012/4/18
We study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac op...
We study the Cheeger constant and Cheeger set for domains obtained as strip-like neighbourhoods of curves in the plane. If the reference curve is complete and finite (a "curved annulus"), then the st...
Curved infinity-algebras and their characteristic classes
Curved infinity-algebras characteristic classes
2010/12/15
In this paper we study a natural extension of Kontsevich’s characteristic class
construction for A∞- and L∞-algebras to the case of curved algebras. These define homology
classes on a variant of his...
Pinching, Pontrjagin classes, and negatively curved vector bundles
Pinching Pontrjagin classes negatively curved vector bundles
2010/11/1
We prove several finiteness results for the class $M_{a,b,G,n}$ of $n$-manifolds that have fundamental groups isomorphic to $G$ and that can be given complete Riemannian metrics of sectional curvature...