nLab Heisenberg homology -- references

Heisenberg homology

Concerning the construction of linear representations of surface-mapping class groups on the homology of configuration spaces of points, twisted by linear representations of the integer Heisenberg group (“Heisenberg homology”):

• Christian Blanchet, Martin Palmer, Awais Shaukat, Heisenberg homology on surface configurations [arXiv:2109.00515]

• Awais Shaukat, Christian Blanchet, Weakly framed surface configurations, Heisenberg homology and Mapping Class Group action, Archiv der Mathematik 120 (2023) 99–109 [doi:10.1007/s00013-022-01793-3, arXiv:2206.11475]

• Christian Blanchet, Martin Palmer, Awais Shaukat: Action of subgroups of the mapping class group on Heisenberg homologies, Contemporary Mathematics 813, AMS (2025) [doi:10.1090/conm/813, arXiv:2306.08614]

• Christian Blanchet: Heisenberg homology of ribbon graphs, in: Essays in Geometry, IRMA Lectures in Math. and Theor. Physics 34, EMS (2023) [doi:10.4171/irma/34/10, arXiv:2401.04477]

and relation to abelian Chern-Simons theory:

• Aleksei Andreev, Anna Beliakova, Christian Blanchet: Abelian TQFTS and Schrödinger local systems [arXiv:2306.10725]

Review:

• Martin Palmer: Representations of the Torelli group via the Heisenberg group, talk at Workshop for Young Researchers in Mathematics – 10th ed. (2021) $[$pdf, pdf]

• Martin Palmer, Mapping class group representations via Heisenberg, Schrödinger and Stone-von Neumann, talk at CQTS (March 2022)

• Christian Blanchet: Heisenberg homologies of surface configurations, talk at Geometric/Topological Quantum Field Theories Workshop @ CQTS NYUAD (2023) [slides:pdf, video:YT]