Exotic R^4 and computing geodesics

Hi folks, I’ve been reading about exotic R^4 and I am very curious to learn more about it!

I have an idea for a project for personal/aesthetic interest and I’m wondering if it’s possible.

I want to be able to make a computer program that could compute “straight” paths in exotic R^4 given an initial position and direction (up to epsilon of error of course).

Is this possible to do? I don’t yet understand enough about differential structures to see whether there is a constructive account of exotic R^4.

Is exotic R^4 a topological vector space in the same way that standard R^4 is? Or does admitting the vector space structure force the standard differential structure?

(Edit: are addition and multiplication both continuous and differentiable in exotic R^4?)

submitted by /u/batterypacks
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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs https://nevinmanimala.com

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