@article {doi:10.1142/S0129055X18500204,
	title = {Principal fibrations over noncommutative spheres},
	journal = {Reviews in Mathematical Physics},
	volume = {30},
	number = {10},
	year = {2018},
	pages = {1850020},
	abstract = {We present examples of noncommutative four-spheres that are base spaces of $SU(2)$-principal bundles with noncommutative seven-spheres as total spaces. The noncommutative coordinate algebras of the four-spheres are generated by the entries of a projection which is invariant under the action of $SU(2)$. We give conditions for the components of the Connes{\textendash}Chern character of the projection to vanish but the second (the top) one. The latter is then a non-zero Hochschild cycle that plays the role of the volume form for the noncommutative four-spheres.},
	doi = {10.1142/S0129055X18500204},
	url = {https://arxiv.org/abs/1804.07032},
	author = {Michel Dubois-Violette and Xiao Han and Giovanni Landi}
}
@inbook {Arici2016,
	title = {Pimsner Algebras and Circle Bundles},
	booktitle = {Noncommutative Analysis, Operator Theory and Applications},
	year = {2016},
	pages = {1{\textendash}25},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Cham},
	abstract = {<p>We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.</p>},
	isbn = {978-3-319-29116-1},
	doi = {10.1007/978-3-319-29116-1_1},
	url = {https://doi.org/10.1007/978-3-319-29116-1_1},
	author = {Francesca Arici and Francesco D{\textquoteright}Andrea and Giovanni Landi},
	editor = {Alpay, Daniel and Cipriani, Fabio and Colombo, Fabrizio and Guido, Daniele and Sabadini, Irene and Sauvageot, Jean-Luc}
}
@article {arici2016pimsner,
	title = {Pimsner algebras and Gysin sequences from principal circle actions},
	journal = {Journal of Noncommutative Geometry},
	volume = {10},
	year = {2016},
	pages = {29{\textendash}64},
	issn = {1661-6952},
	doi = {10.4171/jncg/228},
	url = {http://hdl.handle.net/2066/162951},
	author = {Francesca Arici and Jens Kaad and Giovanni Landi}
}
@article {2005,
	title = {Principal fibrations from noncommutative spheres},
	journal = {Comm. Math. Phys. 260 (2005) 203-225},
	number = {SISSA;68/2004/FM},
	year = {2005},
	abstract = {We construct noncommutative principal fibrations S_\\\\theta^7 \\\\to S_\\\\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\\\\theta^4) \\\\into A(S_\\\\theta^7)$ is an example of a not trivial quantum principal bundle.},
	doi = {10.1007/s00220-005-1377-7},
	url = {http://hdl.handle.net/1963/2284},
	author = {Giovanni Landi and Walter van Suijlekom}
}
