Non-Commutative Geometry of Quantum Spheres

Abstract: In this talk we will begin with a brief discussion on the notion of space in noncommutative geometry. We will recall the notion of quantum group and its homogeneous spaces. Then we concentrate on the specific case of quantum spheres. We will describe the ''geometry'' of these ''spaces'' as we encountered them. That means at various points of time people believed inadequacy of axioms of Connes to tackle these examples and have suggested possible reformulations but we will show without any reformulation one can construct geometries on these spaces which will satisfy many of his axioms