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edit approved May 30, 2019 at 5:56
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edit approved May 30, 2019 at 5:56
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Let $M$ be a finite CW-complex. Let $F$ be a finite rank local system over $M$ with coefficients in any field. Is it true that $dim(H^k(M,F))$$\dim(H^k(M,F))$ is at most the number of $k$-cells times $rank(F)$$\operatorname{rank}(F)$?

If $F$ is the trivial local system then this result is proven in almost any standard textbook in topology (or at least immediately follows from there). I believe that it should be true in the above generality and would be happy to have a reference.

Let $M$ be a finite CW-complex. Let $F$ be a finite rank local system over $M$ with coefficients in any field. Is it true that $dim(H^k(M,F))$ is at most the number of $k$-cells times $rank(F)$?

If $F$ is the trivial local system then this result is proven in almost any standard textbook in topology (or at least immediately follows from there). I believe that it should be true in the above generality and would be happy to have a reference.

Let $M$ be a finite CW-complex. Let $F$ be a finite rank local system over $M$ with coefficients in any field. Is it true that $\dim(H^k(M,F))$ is at most the number of $k$-cells times $\operatorname{rank}(F)$?

If $F$ is the trivial local system then this result is proven in almost any standard textbook in topology (or at least immediately follows from there). I believe that it should be true in the above generality and would be happy to have a reference.

deleted 3 characters in body; added 4 characters in body; added 45 characters in body
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asv
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Let $M$ be a finite CW-complex. Let $F$ be a finite rank local system over $M$ with coefficients in any field. Is it true that $dim(H^k(M,F))$ is at most the number of $k$-cells times $rank(F)$?

If $F$ is the trivial local system then this result is proven in almost any standard textbook in topology (or at least immediately follows from there). I believe that it is should be true in the above generality and would be happy to have a referencewould be happy to have a reference.

Let $M$ be a finite CW-complex. Let $F$ be a finite rank local system over $M$ with coefficients in any field. Is it true that $dim(H^k(M,F))$ is at most the number of $k$-cells times $rank(F)$?

If $F$ is the trivial local system then this result is proven in almost any standard textbook in topology. I believe that it is should be true in the above generality and would be happy to have a reference.

Let $M$ be a finite CW-complex. Let $F$ be a finite rank local system over $M$ with coefficients in any field. Is it true that $dim(H^k(M,F))$ is at most the number of $k$-cells times $rank(F)$?

If $F$ is the trivial local system then this result is proven in almost any standard textbook in topology (or at least immediately follows from there). I believe that it should be true in the above generality and would be happy to have a reference.

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asv
asv
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Cohomogy of local systems over CW-complexes

Let $M$ be a finite CW-complex. Let $F$ be a finite rank local system over $M$ with coefficients in any field. Is it true that $dim(H^k(M,F))$ is at most the number of $k$-cells times $rank(F)$?

If $F$ is the trivial local system then this result is proven in almost any standard textbook in topology. I believe that it is should be true in the above generality and would be happy to have a reference.