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Download Adobe Photoshop Lightroom 5.3 Final (64 bit) [ChingLiu] torrent from software category on Isohunt. Computer software called “adobe lightroom 5.3 final (64 bit) [ChingLiu]”.Q:

With a fiber bundle $E \rightarrow B$, and a fiber (sub)set $D$, is the Mayer-Vietoris sequence the same as the Serre spectral sequence?

I have a fiber bundle $E \rightarrow B$, and a fiber submanifold $D \subset E$, then is the Mayer-Vietoris sequence:
$$
\cdots \rightarrow H^i(B) \oplus H^i(D) \rightarrow H^i(E) \rightarrow H^{i+1}(B, B \cap D) \oplus H^{i+1}(D,B \cap D) \rightarrow \cdots
$$
the same as the Serre spectral sequence?

A:

The Mayer-Vietoris sequence looks like this:
$$\to H^i(E) \to H^i(B)\oplus H^i(D) \to H^{i-1}(B\cap D) \to \cdots$$
where the differentials $d_r$ are given by the intersection cohomology chain complex on the right:
$$\to I^{r-1}(B\cap D) \to I^r(B) \oplus I^r(D) \to I^r(E)\to.$$
Now, the Serre spectral sequence looks like this:
$$\to H^{p+i}(B\cap D) \to H^p(B) \oplus H^i(B\cap D) \to H^{p+1}(B,B\cap D) \to \cdots$$
where the differentials $d_r$ are given by the relative cohomology chain complex on the left.

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