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Michael Albanese
Michael Albanese
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Can one calculatescalculate possible mapping degrees from a connected-sum to another manifold?

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Jens Reinhold
Jens Reinhold
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Added LaTeX, re-formatted the question, edited the phrasing, and added a sentence at the end to motivate the 3-manifold tag. Please roll back (or edit further) if I twisted the question a bit too much.
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Marco Golla
Marco Golla
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Let D(M,N)$D(M,N)$ be the set of all possible mapping degreedegrees of maps from M$M$ to N$N$, M1#M2$M_1\#M_2$ the connected sum of M1 and M2. If D(M1,N) and D(M2,N) (resp. D(N,M1) & D(N,M2)) are already known, can D(M1#M2,N)$M_1$ and (resp$M_2$. D(N,M1#M2)) be calculated?

  1. Can $D(M_1\#M_2,N)$ be calculated in terms of $D(M_1,N)$ and $D(M_2,N)$?
  2. Can $D(N,M_1\#M_2)$ be calculated in terms of $D(N,M_1)$ and $D(N,M_2)$?

Here all manifolds are assumed to be of dim >= 3the same dimension $d \ge 3$. I'm especially interested in the case $d=3$.

Let D(M,N) be the set of all possible mapping degree from M to N, M1#M2 the connected sum of M1 and M2. If D(M1,N) and D(M2,N) (resp. D(N,M1) & D(N,M2)) are already known, can D(M1#M2,N) (resp. D(N,M1#M2)) be calculated? Here all manifolds are assumed of dim >= 3.

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 $M_2$.

  1. Can $D(M_1\#M_2,N)$ be calculated in terms of $D(M_1,N)$ and $D(M_2,N)$?
  2. Can $D(N,M_1\#M_2)$ be calculated in terms of $D(N,M_1)$ and $D(N,M_2)$?

Here all manifolds are assumed to be of the same dimension $d \ge 3$. I'm especially interested in the case $d=3$.

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Invy S.
Invy S.
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