We define quantum lens spaces as 'direct sums of line bundles' and exhibit them as 'total
spaces' of certain principal bundles over quantum projective spaces. For each of these …

The $ K_0 $-group of the C*-algebra of multipullback quantum complex projective plane is
known to be $\mathbb {Z}^ 3$, with one generator given by the C*-algebra itself, one given …

In this thesis I discuss some results on the noncommutative (spin) geometry of quantum
principal G-bundles. The first part of the thesis is devoted to the study of spectral triples over …

The Pullbacks of Principal Coactions Page 1 Documenta Math. 1025 The Pullbacks of Principal
Coactions Piotr M. Hajac, Elmar Wagner Received: December 31, 2013 Revised: August 9 …

Let H be the C*-algebra of a non-trivial compact quantum group acting freely on a unital C*-
algebra A. It was recently conjectured that there does not exist an equivariant …

We equip the multi-pullback $ C^* $-algebra $ C (S^ 5_H) $ of a noncommutative-
deformation of the 5-sphere with a free $ U (1) $-action, and show that its fixed-point …

We prove that the class of principal coactions is closed under one-surjective pullbacks in an
appropriate category of algebras equipped with left and right coactions. This allows us to …

Weighted circle actions on the quantum Heeqaard 3-sphere are considered. The fixed point
algebras, termed quantum weighted Heegaard spheres, and their representations are …

Principal circle bundles and Gysin sequences play a crucial role in mathematical physics, in
particular in Chern-Simons theories and T-duality. This works focuses on the …

By a diagonal embedding of $ U (1) $ in $ SU_q (m) $, we prolongate the diagonal circle
action on the Vaksman-Soibelman quantum sphere $ S^{2n+ 1} _q $ to the $ SU_q (m) …