Real life applications of Topology
From wikipatents:
http://www.wikipatents.com/US-Patent-3991631/woven-endless-belt-of-a-spliceless-and-mobius-strip-construction LINK DEAD
patents.com link
Robert Ghrist uses algebraic topology to improve sensor networks and robotics.
Twisted K-Theory is used to classify D-branes in string theory.
See "Topological Insulators", an invention that takes electronics to a new phase.
http://en.wikipedia.org/wiki/Topological_insulator