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Normal Invariants of Lens Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
We show that normal and stable normal invariants of polarized homotopy equivalences of lens spaces $M=\,L({{2}^{m}};\,{{r}_{1}},...,\,{{r}_{n}})$ and
$N\,=\,L({{2}^{m}};\,{{s}_{1}},...,{{s}_{n}})$ are determined by certain
$\ell $-polynomials evaluated on the elementary symmetric functions
${{\sigma }_{i}}\,(r_{1}^{2},...,r_{n}^{2})$ and
${{\sigma }_{i}}(s_{1}^{2},...,s_{n}^{2})$. 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.
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- Copyright © Canadian Mathematical Society 1998
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