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Zap. Nauchn. Sem. POMI, 2013, Volume 415, Pages 163–193 (Mi znsl5693)  

Atiyah–Patodi–Singer $\eta$-invariant and invariants of finite degree

A. N. Trefilov

St. Petersburg State University, St. Petersburg, Russia

Abstract: We consider the problem of computing the degree of invariants of the form $\eta\bmod A$, where $\eta$ is the Atiyah–Patodi–Singer invariant considered on smooth compact oriented three-dimensional submanifolds of $\mathbb R^n$ and $A$ is an additive subgroup of $\mathbb R$. We use the functional definition of invariants of finite degree. (A similar approach is used in the paper “Quadratic property of the rational semicharacteristic” by S. S. Podkorytov.) The main results are as follows. If $1\notin A$, the degree is infinite. If $\frac13\in A$, the degree equals one.

Key words and phrases: Atiyah–Patodi–Singer $\eta$-invariant, invariants of finite degree.

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English version:
Journal of Mathematical Sciences (New York), 2016, 212:5, 622–642

UDC: 514.76
Received: 05.03.2013

Citation: A. N. Trefilov, “Atiyah–Patodi–Singer $\eta$-invariant and invariants of finite degree”, Geometry and topology. Part 12, Zap. Nauchn. Sem. POMI, 415, POMI, St. Petersburg, 2013, 163–193; J. Math. Sci. (N. Y.), 212:5 (2016), 622–642

Citation in format AMSBIB
\Bibitem{Tre13}
\by A.~N.~Trefilov
\paper Atiyah--Patodi--Singer $\eta$-invariant and invariants of finite degree
\inbook Geometry and topology. Part~12
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 415
\pages 163--193
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5693}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 212
\issue 5
\pages 622--642
\crossref{https://doi.org/10.1007/s10958-016-2694-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953265682}


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