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# Normal invariants of lens spaces

Published:1998-09-01
Printed: Sep 1998
• Carmen M. Young
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## Abstract

We show that normal and stable normal invariants of polarized homotopy equivalences of lens spaces $M = L(2^m;\r)$ and $N = L(2^m;\s)$ are determined by certain $\ell$-polynomials evaluated on the elementary symmetric functions $\sigma_i(\rsquare)$ and $\sigma_i(\ssquare)$. Each polynomial $\ell_k$ appears as the homogeneous part of degree $k$ in the Hirzebruch multiplicative $L$-sequence. When $n = 8$, the elementary symmetric functions alone determine the relevant normal invariants.
 MSC Classifications: 57R65 - Surgery and handlebodies 57S25 - Groups acting on specific manifolds