Non-semisimple 3-manifold invariants derived from the Kauffman bracket

Marco De Renzi, Jun Murakami

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of sl2 using purely combinatorial meth-ods based on Temperley–Lieb algebras and Kauffman bracket polynomials. These invariants can be understood as a first-order extension of Witten–Reshetikhin–Turaev invariants, which can be reformulated following our approach in the case of rational homology spheres.

Original languageEnglish
Pages (from-to)255-333
Number of pages79
JournalQuantum Topology
Issue number2
Publication statusPublished - 2022


  • Kauffman bracket
  • Quantum invariants
  • Temperley–Lieb algebras
  • quantum groups

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology


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