On Wall manifolds with (\(\epsilon\) )-free involutions
Wall manifolds are manifolds M with a classifying map \(\alpha: M\to {\mathbb{R}}P^{\infty}\), with \(\alpha(M)\subset {\mathbb{R}}P^ 1\), for the determinant line bundle det \(\tau_ M\) of the tangent bundle \(\tau_ M\). Let \(W_*\) be the bordism ring of Wall manifolds, and \(W_*^+({\mathbb{Z}}_ 2)\) (resp. \(W_*^-({\mathbb{Z}}_ 2))\) be the bordism group of Wall manifolds M with fixed point free involution \(\mu\) with \({\tilde \alpha}\circ \det d\mu ={\tilde \alpha}\) (resp. \({\tilde \alpha}\circ \det d\mu =-{\tilde \alpha})\), where \({\tilde \alpha}\) is a bundle map of det \(\tau_ M\) which covers \(\alpha\) and \(d\mu\) is the differential of \(\mu\). The paper under review explicitly presents bases of \(W^+_*({\mathbb{Z}}_ 2)\) and \(W^-_*({\mathbb{Z}}_ 2)\) as \(W_*\)- modules. It also presents bases of their images in the unoriented bordism group of fixed point free involutions.
bordism group of Wall manifolds with fixed point free involution
unoriented bordism group of fixed point free involutions
scientific article; zbMATH DE number 4009350