The short answer is: sorta. Robert Ghrist has done some work applying topological work to "real-world" problems [0]. I use scare quotes here because while his w

The short answer is: sorta. Robert Ghrist has done some work applying topological work to "real-world" problems [0]. I use scare quotes here because while his work is interesting, I'm not sure it allows industry to do anything it couldn't have done before. There's also quite a large body of (academic) work applying topological methods to robotics. Robots have complex configuration spaces and apparently topological methods can help us understand those spaces. [0] https://www2.math.upenn.edu/~ghrist/notes.html https://www2.math.upenn.edu/~ghrist/notes.html