What is the relation between the genus of X and the genus of Y when there is a d-to-1 map from X to Y? (Assume that around each y in Y we can find a disk whose preimage consists of d disks.) Do we have genus(X) = d genus(Y) ? Jim Propp On Mon, Nov 2, 2020 at 7:23 PM Allan Wechsler <acwacw@gmail.com> wrote:
Sorry, I think g-1 is what I meant. X = 2-2g = 2(1-g) = -2(g-1), so it would be g-1 that would correspond to the Euler characteristic.
On the other hand, g+1 is significant for the polyhedral models: a thick spherical shell with n holes drilled in it has genus n-1, so g+1 = n.
I don't know if there is any actual math here, or if I'm just being deluded by numerology.
On Mon, Nov 2, 2020 at 12:42 PM Marc LeBrun <mlb@well.com> wrote:
=Allan Wechsler I expect the genus plus one to be a nicely divisible number.
? 73 *plus* one is 74, but 73 *minus* one is 72, which seems much more bigly nicely?
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