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Normal Invariants of Lens Spaces

Published online by Cambridge University Press:  20 November 2018

Carmen M. Young
Carmen M. Young*
Affiliation:
Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139-4307 USA
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Abstract

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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.

Keywords

57R6557S25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 3 , 01 September 1998 , pp. 374 - 384
Copyright
Copyright © Canadian Mathematical Society 1998

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