A converse of the Borel formula

Dotzel, Ronald M.

doi:10.1090/S0002-9947-1979-0530056-0

A converse of the Borel formula
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by Ronald M. Dotzel PDF

Trans. Amer. Math. Soc. 250 (1979), 275-287 Request permission

Abstract:

When an elementary Abelian p-group acts on a ${Z_p}$-homology sphere (p a prime), it is known that the Borel formula must hold. Here we ask that the Borel formula hold and determine how this restricts, homologically, the type of space which can occur, assuming spherical fixed sets and connectedness. This is done by constructing a linear model of the action and an equivariant map to the model, the mapping cone of which yields certain homological information.

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