MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

It is given in Progress in mathematics 62, Guillou and Marin book. In the proof of Lemma 4, They choose $\alpha$ and $r\in \mathbb{N}$ such that $h^r_*\colon H_1(X;Z_p)\to H_1(X;Z_p)$ satisfies $h^r_*(\alpha)=\alpha$ and conclude that $X\to X$ can be lifted to $\tilde{X}\to \tilde{X}$. Since $\tilde{X}$ is a convering space of $X$, I agree that it is enought to show that the primary obstruction $[\theta(h^r\circ p)]\in H^1(X;Z_p)$ vanishes. (Is this local coefficient system is trivial?) Why $h^r_*\colon H_1(X;Z_p)\to H_1(X;Z_p)$ satisfying $h^r_*(\alpha)=\alpha$ ensures that the existence of lifting $\tilde{h}\colon \tilde{X}\to \tilde{X}$ and why $\tilde{X}\to \tilde{X}/\tilde{h}$ is infinite covering?

Thank you

share|cite|improve this question
You might want to supply more context. As written, your question assumes readers remember terminology from a particular paper. I suspect this paper is the one where Casson and Gordon define their eponymous invariants ? – Ryan Budney Jul 14 '10 at 0:05

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.