## Free involutions on $E_ {4m}$ lattices

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- by Wojtek Jastrzebowski
- Proc. Amer. Math. Soc.
**123**(1995), 1941-1945 - DOI: https://doi.org/10.1090/S0002-9939-1995-1254844-5
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## Abstract:

We determine all the conjugacy classes of traceless involutions on the ${E_{4m}}$ lattices. In particular, we show that for every $m > 2$ there exist precisely two nonconjugate involutions which induce free ${\mathbf {Z}}[{{\mathbf {Z}}_2}]$-module structures. By inspecting the parity of the ${E_{4m}}$ form twisted by any such involution, we deduce that a closed, simply connected, topological 4-manifold with intersection form ${E_{4m}}$ supports a locally linear involution if and only if*m*is odd and the Kirby-Siebenmann invariant of the manifold is trivial.

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## Bibliographic Information

- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**123**(1995), 1941-1945 - MSC: Primary 57N13; Secondary 11H06
- DOI: https://doi.org/10.1090/S0002-9939-1995-1254844-5
- MathSciNet review: 1254844