Elliptic genera, modular forms over \(KO_ *\), and the Brown-Kervaire invariant

DOI10.1007/BF02571343zbMath0714.57013OpenAlexW2046712288MaRDI QIDQ750959

Serge Ochanine

Publication date: 1991

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174225

zbMATH Keywords

spin manifoldAtiyah invariantBrown-Kervaire invariantKO-characteristic numbermodular form over \(KO_ *\)refined elliptic genus

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Elliptic genera (58J26) Other types of cobordism (57R90) Topological (K)-theory (55N15)

Related Items

\(\mathbf H\mathbf P^ 2\)-bundles and elliptic homology ⋮ Spin bordism and elliptic homology ⋮ Differential KO-theory: constructions, computations, and applications ⋮ On mod 2 and higher elliptic genera ⋮ Topological modular forms with level structure ⋮ Applications of the Ochanine genus ⋮ An algebraic description of the elliptic cohomology of classifying spaces ⋮ The Dirac-Ramond operator on loops in flat space ⋮ Circle bundles, adiabatic limits of \(\eta\)-invariants and Rokhlin congruences

Cites Work

• Sur les genres multiplicatifs définis par des intégrales elliptiques. (On multiplicative genera defined by elliptic integrals)
• Circle actions on spin manifolds and characteristic numbers
• Elliptic modular functions and elliptic genera
• Applications of the Ochanine genus
• Relations among characteristic numbers. II
• On complex-spin manifolds
• The relation of cobordism to K-theories
• Generalizations of the Kervaire invariant
• On the Rigidity Theorems of Witten
• Riemann surfaces and spin structures
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