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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Free involutions on $E_ {4m}$ lattices

Author: Wojtek Jastrzebowski
Journal: Proc. Amer. Math. Soc. 123 (1995), 1941-1945
MSC: Primary 57N13; Secondary 11H06
MathSciNet review: 1254844
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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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Article copyright: © Copyright 1995 American Mathematical Society