On the topological contents of η–invariants

Bunke, Ulrich¹

¹ Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg, Germany

Geometry & topology, Tome 21 (2017) no. 3, pp. 1285-1385.

Résumé

We discuss a universal bordism invariant obtained from the Atiyah–Patodi–Singer $\eta$–invariant from the analytic and homotopy-theoretic point of view. Classical invariants like the Adams $e$–invariant, $\rho$–invariants and $String$–bordism invariants are derived as special cases. The main results are a secondary index theorem about the coincidence of the analytic and topological constructions and intrinsic expressions for the bordism invariants.

Détail

DOI : 10.2140/gt.2017.21.1285

Classification : 58J28
Keywords: eta invariant, $K$–theory, bordism

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