Subject: Re: Hopf postings & refinement
Date: Tue, 30 Apr 2002 12:50:50 -0500
From: Frank Connolly
To: Don Davis
An Answer to Stasheff's Question:
The rational group ring, Q[Z/2Z] splits as Q^{+} X Q^{-}. By
(twisted) Poincare duality, H^k(Y;Q^{-}) = H_{n-k)(Y;Q). We
therefore get:
H^k(X;Q)= H^k(Y; Q[Z/2Z])= H^k(Y;Q) X H^{k}(Y;Q^{-})=H^k(Y;Q) X
H_n-k(Y;Q), from which:
b_k(X) = b_k(Y) + b_{n-k}(Y) follows.
--
Frank Connolly
Professor
Department of Mathematics
Room 169 Hurley
University of Notre Dame
Notre Dame IN, 46556-4618
(219)631-6571