Institute of Mathematics for Industry

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On mod 2 arith- metic Dijkgraaf-Witten invariants for certain real quadratic number fields


Hold Date 2020-01-31 16:00~2020-01-31 17:00

Place Lecture Room M W1-C-513, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Hikaru HIRANO (Kyushu university)

Abstract:
In recent years, based on the analogies in arithmetic topology, Minhyong Kim initiated to study arithmetic Chern-Simons theory, and introduced an arithmetic analogy for totally imaginary number fields of the Dijkgraaf-Witten invariants for 3-manifolds. In this talk, we extend Kim’s definition for any number field, by using the modified etale cohomology groups which take real places into account. We then show explicit formulas of mod 2 arithmetic Chern-Simons and Dijkgraaf-Witten invariants for certain real quadratic fields. We also show a topological analogue of our results.