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Euler and Maslov cocycles. (Cocycles d’Euler et de Maslov.) (French) Zbl 0894.55006
This elegant paper takes its inspiration partly from one by M. F. Atiyah [ibid. 278, 335-380 (1987; Zbl 0648.58035)], in which a diverse set of numerical functions on \(\text{SL}_2(\mathbb{Z})\) were unified. There is an analogy between the Dedekind \(\eta\)-function of that paper, the defect of the Hirzebruch signature formula, and a function due to Rademacher, and the authors exploit this to study these invariants and others by means of bounded cohomology 2-cocycles. The strategy is to show that the coboundary of the functions of interest is a bounded 2-cocycle and that the bounded cohomology class obtained is unique for a uniformly perfect group like \(\text{SL}_2\) or \(\text{Sp}_{2n}\).

MSC:
55U99 Applied homological algebra and category theory in algebraic topology
11F20 Dedekind eta function, Dedekind sums
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