@article {2014,
	title = {Dirac operators on noncommutative principal circle bundles},
	number = {International Journal of Geometric Methods in Modern Physics;volume 11; issue 1; article number 1450012;},
	year = {2014},
	publisher = {World Scientific Publishing},
	abstract = {We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ {\textrightarrow} S2.},
	doi = {10.1142/S0219887814500121},
	url = {http://urania.sissa.it/xmlui/handle/1963/35125},
	author = {Andrzej Sitarz and Alessandro Zucca and Ludwik Dabrowski}
}
@article {2013,
	title = {Curved noncommutative torus and Gauss--Bonnet},
	journal = {Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518},
	number = {arXiv:1204.0420v1;},
	year = {2013},
	note = {The article is composed of 13 pages and is recorded in PDF format},
	publisher = {American Institute of Physics},
	abstract = {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 operator D, which is a
differential operator with coefficients in the commutant of the (smooth)
algebra A_\theta of T_\theta. We show, up to the second order in perturbation,
that the zeta-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We
also calculate first two terms of the perturbative expansion of the
corresponding local scalar curvature.},
	keywords = {Geometry},
	doi = {10.1063/1.4776202},
	url = {http://hdl.handle.net/1963/7376},
	author = {Ludwik Dabrowski and Andrzej Sitarz}
}
@article {2013,
	title = {Noncommutative circle bundles and new Dirac operators},
	journal = {Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130},
	number = {arXiv:1012.3055v2;},
	year = {2013},
	note = {This article is composed of 25 pages and is recorded in PDF format},
	publisher = {Springer},
	abstract = {We study spectral triples over noncommutative principal U(1) bundles. Basing
on the classical situation and the abstract algebraic approach, we propose an
operatorial definition for a connection and compatibility between the
connection and the Dirac operator on the total space and on the base space of
the bundle. We analyze in details the example of the noncommutative three-torus
viewed as a U(1) bundle over the noncommutative two-torus and find all
connections compatible with an admissible Dirac operator. Conversely, we find a
family of new Dirac operators on the noncommutative tori, which arise from the
base-space Dirac operator and a suitable connection.},
	keywords = {Quantum principal bundles},
	doi = {10.1007/s00220-012-1550-8},
	url = {http://hdl.handle.net/1963/7384},
	author = {Ludwik Dabrowski and Andrzej Sitarz}
}
@article {2005,
	title = {The Dirac operator on SU_q(2)},
	journal = {Commun. Math. Phys. 259 (2005) 729-759},
	number = {arXiv:math/0411609;},
	year = {2005},
	note = {v2: minor changes},
	publisher = {Springer},
	abstract = {We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the
spectrum of the operator D is the same as that of the usual Dirac operator on
the 3-dimensional round sphere. The presence of an equivariant real structure J
demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.},
	doi = {10.1007/s00220-005-1383-9},
	url = {http://hdl.handle.net/1963/4425},
	author = {Ludwik Dabrowski and Giovanni Landi and Andrzej Sitarz and Walter van Suijlekom and Joseph C. Varilly}
}
@article {2005,
	title = {The local index formula for SUq(2)},
	journal = {K-Theory 35 (2005) 375-394},
	number = {SISSA;01/2005/FM},
	year = {2005},
	abstract = {We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.},
	doi = {10.1007/s10977-005-3116-4},
	url = {http://hdl.handle.net/1963/1713},
	author = {Walter van Suijlekom and Ludwik Dabrowski and Giovanni Landi and Andrzej Sitarz and Joseph C. Varilly}
}
@article {2005,
	title = {The spectral geometry of the equatorial Podles sphere},
	journal = {C. R. Math. 340 (2005) 819-822},
	number = {SISSA;71/2004/FM},
	year = {2005},
	abstract = {We propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties.},
	doi = {10.1016/j.crma.2005.04.003},
	url = {http://hdl.handle.net/1963/2275},
	author = {Ludwik Dabrowski and Giovanni Landi and Mario Paschke and Andrzej Sitarz}
}
@article {2001,
	title = {Dirac operator on the standard Podles quantum sphere},
	journal = {Noncommutative geometry and quantum groups (Warsaw 2001),49,Banach Center Publ., 61, Polish Acad.Sci., Warsaw,2003},
	number = {SISSA;98/2002/FM},
	year = {2001},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/1668},
	author = {Ludwik Dabrowski and Andrzej Sitarz}
}
