Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The cofibre of the transfer map


Author: Larry W. Cusick
Journal: Proc. Amer. Math. Soc. 93 (1985), 561-566
MSC: Primary 55R20; Secondary 55R12, 57S17
MathSciNet review: 774023
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose a finite group $ G$ acts freely on a finite complex $ X$ with orbit space $ B$. The cofibre $ \mathcal{C}$ of the transfer map, is defined by the cofibre sequence $ {\Sigma ^0}{B_ + }\mathop \to \limits^{{\text{tr}}} {\Sigma ^0}{X_ + } \to \mathcal{C}$. We show that there is a spectral sequence $ H_G^p(X;\tilde M \otimes {h^q}) \Rightarrow {h^{p + q}}(\mathcal{C})$ for any cohomology theory $ {h^ * }$, where $ \tilde M$ is the reduced regular $ {\mathbf{Z}}$-representation for $ G$. As a special case we prove that $ {H^ * }(\mathcal{C};{\mathbf{Z}}_2)$ is a free $ {H^ * }(B;{{\mathbf{Z}}_2})$-module on a zero-dimensional class for any two-fold cover.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55R20, 55R12, 57S17

Retrieve articles in all journals with MSC: 55R20, 55R12, 57S17


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0774023-9
PII: S 0002-9939(1985)0774023-9
Article copyright: © Copyright 1985 American Mathematical Society