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Results tagged with euler-characteristics
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user 290
8
votes
Triviality of certain vector bundles
Yes, lots. You can see this by computing characteristic classes using the splitting principle. Let me write $T$ for the tangent bundle and $S^2 T$ for its symmetric square. If we write $T = L_1 + \dot …
- 118k
25
votes
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What is the Euler characteristic of a mapping space?
This Euler characteristic usually won't be well-defined. For example, take $A = S^1$ and $B = S^3$. Then the mapping space $[A, B]$ is the free loop space $L S^3$, which decomposes as a product
$$L S …
- 118k