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A monstrous(?) complex hyperbolic orbifold

By Tathagata Basak

Appears in collection : Complex Hyperbolic Geometry and Related Topics / Autour de la géométrie hyperbolique complexe

I will report on progress with Daniel Allcock on the ”Monstrous Proposal”, namely the conjecture: Complex hyperbolic 13-space, modulo a particular discrete group, and with orbifold structure changed in a simple way, has fundamental group equal to (MxM)(semidirect)2, where M is the Monster finite simple group. Our progress is a proof that this orbifold fundamental group has generators that satisfy defining relations for (MxM)(semidirect) 2. It follows that either the monstrous proposal is true, or else the orbifold fundamental group collapses to Z/2. The generators and relations are extremely natural from the complex hyperbolic perspective, keeping hopes high for the conjecture.

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Citation data

  • DOI 10.24350/CIRM.V.19936403
  • Cite this video Basak Tathagata (7/7/22). A monstrous(?) complex hyperbolic orbifold. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19936403
  • URL https://dx.doi.org/10.24350/CIRM.V.19936403


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