ADO invariants directly from partial traces of homological representations

2020/07/30 by Cristina Ana-Maria Anghel, Anghel, Cristina Ana-Maria
Mathematics · #16T05 #16T25 #20F36 #57M25 #57M27 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2007.15616

openalex publication_date 2020/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The ADO invariants are a sequence of non-semisimple quantum invariants coming from the representation theory of the quantum group U_q(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.

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