Normal Invariants of Lens Spaces

Young, Carmen M.

Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 374-384

Résumé

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.

Détail

DOI : 10.4153/CMB-1998-050-6

Mots-clés : 57R65, 57S25