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Results tagged with topological-manifolds
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user 40804
18
votes
Accepted
Is there a closed non-smoothable 4-manifold with zero Euler characteristic?
The Kirby-Siebenmann invariant in $H^4(M;\Bbb Z/2)$, an obstruction to smoothability, is additive under connected sum in dimension 4. In even dimensions, $\chi(M \# N) = \chi(M) + \chi(N) -2$.
To co …
- 9,580
14
votes
Accepted
Is the top Stiefel-Whitney number of a topological manifold the Euler characteristic mod two?
As you say, we define $w_n = \sum \text{Sq}^i \nu_{n - i}$, where $\nu_{n-i}$ is the Wu class, the class such that $\nu_{n-i} \cup c = \text{Sq}^{n-i} c$ for $c \in H^{i}$. So as a corollary we have $ …
- 9,580