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Homotopy theory, homological algebra, algebraic treatments of manifolds.

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Can one calculate possible mapping degrees from a connected-sum to another manifold?

Let $D(M,N)$ be the set of all possible degrees of maps from $M$ to $N$, $M_1\#M_2$ the connected sum of $M_1$ and $M_2$. Can $D(M_1\#M_2,N)$ be calculated in terms of $D(M_1,N)$ and $D(M_2,N)$ …
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