This looks like a gem, thanks!

Under my elbow as I type is a small introductory book called Topology for Computing, which I’d recommend to anyone trying to investigate such links, for its concise clarity and elegant figures.

https://www.amazon.com/Computing-Cambridge-Monographs-Comput...

Gunnar wrote a review article a few years ago called Topology and Data (http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01...). It is an amazingly well written and accessible paper for a technical audience.

Pair it with Afra's book (http://www.amazon.com/Computing-Cambridge-Monographs-Computa...)

I recommend Afra's book:

http://www.amazon.com/Computing-Cambridge-Monographs-Computa...

Happy to help if you need it!