New York Journal of Mathematics
Volume 30 (2024), 481-501


Cristina Ana-Maria Anghel

ADO invariants directly from partial traces of homological representations

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Published: March 31, 2024.
Keywords: Quantum invariants, homological representations, topological models.
Subject [2020]: 57K10, 57K14.

The ADO invariants are a sequence of non-semisimple quantum invariants coming from the representation theory of the quantum group Uq(sl(2)) at roots of unity. Ito showed that these invariants are sums of traces of quotients of homological representations of braid groups (truncated Lawrence representations). In this paper we show a direct homological formula for the ADO invariants, as sums of partial traces of Lawrence type representations, without further truncations.


This paper was prepared at the University of Oxford, and I acknowledge the support of the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 674978). I am grateful to the anonymous referee for useful comments and suggestions about an earlier version of this paper.

Author information

Cristina Ana-Maria Anghel
University of Geneva, Section de mathematiques
Rue du Conseil-General 7-9, CH 1205 Geneva, Switzerland;
Institute of Mathematics "Simion Stoilow" of the Romanian Academy
21 Calea Grivitei Street, 010702 Bucharest, Romania.