On the Cohomological Crepant Resolution Conjecture for the complexified Bianchi orbifolds

Perroni, Fabio; Rahm, Alexander

doi:10.2140/agt.2019.19.2715

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On the Cohomological Crepant Resolution Conjecture for the complexified Bianchi orbifolds

Perroni, Fabio; Rahm, Alexander

In press • In Algebraic and Geometric Topology

Peer Reviewed verified by ORBi

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https://hdl.handle.net/10993/28987

DOI
10.2140/agt.2019.19.2715

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Keywords :

55N32, Orbifold cohomology

Abstract :

[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.

Research center :

University of Trieste, the group GNSAGA of INDAM

Disciplines :

Mathematics

Author, co-author :

Perroni, Fabio; Universita di Trieste > Department of Mathematics and Geosciences

Rahm, Alexander ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit

External co-authors :

yes

Language :

English

Title :

On the Cohomological Crepant Resolution Conjecture for the complexified Bianchi orbifolds

Publication date :

In press

Journal title :

Algebraic and Geometric Topology

ISSN :

1472-2747

eISSN :

1472-2739

Publisher :

Geometry & Topology Publications, United Kingdom

Peer reviewed :

Peer Reviewed verified by ORBi

Name of the research project :

"Geometria delle varieta' algebriche", FRA 2015

Funders :

PRIN 2015EYPTSB-PE1 and Gabor Wiese's Université du Luxembourg grant AMFOR

Available on ORBilu :

since 05 December 2016

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