Why is (algebraic) topology important?

  • Thread starter octol
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Been studying some basic algebraic topology lately. Altough interesting in itself, it would also be interesting to hear if it has any important applications in other branches of mathematics or in other fields (physics?).
 

matt grime

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led to the development of category theory...

but seriously, a sound knowledge of algebraic topology is essential to many (most?) areas of mathematics for it has important consequences in analysis and physics, eg the Atiyah-Singer Index theorem, or mathematical physics (topological quantum field theory for one), or dynamical systems (chaos theory to those who like labels), or algebraic geometry (cryptography in some sense), or even in the study of liquid crystals (don't know anything about that but i heard a rumour once).
 

mathman

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It is my understanding that string theory makes heavy use of algebraic topology, although I must admit I know very little about either.
 

mathwonk

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topology is important and algebraic methods render topology computable.
 

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