TITLE: Real life applications of Topology
QUESTION [127 upvotes]: The other day I and my friend were having an argument. He was saying that there is no real life application of Topology at all whatsoever. I want to disprove him, so posting the question here.
What are the various real life applications of topology?

REPLY [3 votes]: Pebbles on Mars Likely Traveled Miles Down a Riverbed

The development of a quantitative understanding of pebble shapes began with the work of Domokos, whose research was triggered by the discovery of the Gömböc, a curious three-dimensional object with just two static balance points. A Gömböc shape self-rights on a horizontal surface just like a Weeble Wobble, however, it has no added bottom weight. The self-righting property is the result of the shape alone, which is determined to 0.01 percent accuracy by its unique mechanical properties.
As the number of static balance points on an object tends to be reduced during natural abrasion, the Gömböc represents the ultimate goal of this process and illustrates how shape alone may carry vital information on natural history. Domokos soon realized that recent pioneering work in pure mathematics—the proof of the elusive Poincaré conjecture—could be adapted to describe the geometry of three-dimensional structures and how these shapes evolve.

refers to Universal characteristics of particle shape evolution by bed-load chipping, Science Advances  28 Mar 2018.