Reference : On the Cohomological Crepant Resolution Conjecture for the complexified Bianchi orbifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
On the Cohomological Crepant Resolution Conjecture for the complexified Bianchi orbifolds
Perroni, Fabio [Universita di Trieste > Department of Mathematics and Geosciences]
Rahm, Alexander mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
In press
Algebraic and Geometric Topology
Geometry & Topology Publications
United Kingdom
[en] 55N32, Orbifold cohomology
[en] We give formulae for the Chen--Ruan orbifold cohomology for the orbifolds given by a Bianchi group acting on complex hyperbolic 3-space. The Bianchi groups are the arithmetic groups PSL_2(A), where A is the ring of integers in an imaginary quadratic number field.
The underlying real orbifolds which help us in our study, given by the action of a Bianchi group on real hyperbolic 3-space (which is a model for its classifying space for proper actions),
have applications in physics.

We then prove that, for any such orbifold, its Chen-Ruan orbifold cohomology ring
is isomorphic to the usual cohomology ring of any crepant resolution of its coarse moduli space.
By vanishing of the quantum corrections, we show that this result fits in with Ruan's Cohomological Crepant Resolution Conjecture.
University of Trieste, the group GNSAGA of INDAM
PRIN 2015EYPTSB-PE1 and Gabor Wiese's Université du Luxembourg grant AMFOR

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