Perron's conjecture on the mod-p extension of the Casson invariant
Perron's conjecture on the mod-p extension of the Casson invariant
Let and let be prime. Let be the mod- Torelli group, the Torelli group, and the subgroup generated by -powers of Dehn twists. For with , where and , define by
Perron's conjecture. The map is a well-defined invariant on . Perron proposed this as an extension of the Casson invariant to the mod- Torelli group. The supplied text does not state whether the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Ricard Riba and Wolfgang Pitsch, “Invariants of Z/p-Homology 3-Spheres from the Abelianization of the Level-p Mapping Class Group”, arXiv:2103.15519 (2023).
Additional references
2 papers in this index state this conjecture (2020–2021). The statement above is taken from the most recent of them; the others are arXiv:2002.10589.
Progress summary
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