In the book

> Farber, Michael. *Invitation to topological robotics*. European Mathematical Society, 2008,

Farber uses C&P (cut & paste) surgery and the Grothendiek ring $\mathfrak{C}$&$\mathfrak{P}$
to compute Euler characteristics of polyhedral configuration spaces (pp.55-56):
<hr />
&nbsp;
&nbsp;
&nbsp;
&nbsp;
![C&P][1]
<hr />
(This is not a topic with which I am intimately familiar, but I offer it as
a connection between robotics and Grothendiek's work.)

  [1]: https://i.sstatic.net/h0r6f.png