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Nov
19 |
awarded | Commentator |
Nov
19 |
comment |
Reference request for cohomology of coverings
@BenWieland. It sounds like there is no reasonable statement along the lines of the original question then. This is very enlightening. Many thanks, Ben, as well as Matthias and Dan. |
Nov
18 |
comment |
Reference request for cohomology of coverings
This answer was meant to give an alternative description of Matthias's answer for cyclic coverings. As Ben points out, this does not suffice for the inductive step and there is no hope of extending this construction even to ${\mathbb{Z}}^2$-coverings without additional assumptions. |
Nov
18 |
comment |
Reference request for cohomology of coverings
Is there a statement in the spirit of the original one which is true? It is true if the rank of $G$ is at most one. Is it true if the abelianization of the commutator subgroup of $\pi_1(B)$ is finite? or perhaps even the commutator subgroup itself is finite? |
Nov
18 |
comment |
Reference request for cohomology of coverings
Thank you, Ben. I think I see where my thinking with the induction went wrong. $H^*(\hat{B})^{\mathbb Z}$ comes from $H^*(\hat{B}/{\mathbb Z})$, but only $H^*(\hat{B}/{\mathbb Z})^{\mathbb Z}$ comes from $H^*(\hat{B}/{\mathbb Z}^2)$. More relevantly, one needs to show that $H^*(\hat{B})^{\mathbb{Z}^2}$ comes from $H^*(\hat{B}/{\mathbb{Z}})^{\mathbb{Z}}$, and there was nothing in the inductive step about some auxiliary group. |
Nov
16 |
answered | Reference request for cohomology of coverings |
May
31 |
awarded | Critic |
Apr
14 |
comment |
On the proof of Robert Lipshitz's formula on Maslov index.
Why not just e-mail, Robert? |
Mar
31 |
answered | Difference between parallel transport and derivative of the exponential map |
Feb
19 |
awarded | Enthusiast |
Jan
29 |
answered | Analytic curve on Riemann surface |
Jan
28 |
revised |
Tubular neighborhoods of chains
added 36 characters in body |
Jan
28 |
revised |
Tubular neighborhoods of chains
added 156 characters in body; deleted 103 characters in body |
Jan
28 |
answered | Tubular neighborhoods of chains |
Jan
24 |
awarded | Scholar |
Jan
24 |
awarded | Supporter |
Jan
24 |
awarded | Student |
Jan
21 |
awarded | Editor |
Jan
21 |
revised |
Orientations for pseudoholomorphic curves with totally real boundary condition
added 773 characters in body |
Jan
21 |
answered | Orientations for pseudoholomorphic curves with totally real boundary condition |