4 ms·

> why can the earth can be treated as a topoligical insulator I am missing something here. Topology is a field of mathematics that studies the properties of ob

> why can the earth can be treated as a topoligical insulator I am missing something here. Topology is a field of mathematics that studies the properties of objects that do not change under continuous deformations. So before asking why can Earth be treated as a topological something - one should specify what topology he is looking at, that is what continuous deformations of Earth he is talking about. So - what continuous deformations of Earth are you talking about?

deleted 3y ago
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zornthewise 3y ago
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kergonath 3y ago
That’s a culture difference issue. A topological insulator is a kind of material with specific properties (heavily simplified, that its inside is an electric insulator and its surface is an electric conductor). That’s where the topological aspect comes from. It has nothing to do with topology in mathematics except the name.
- staunton 3y ago
  > It has nothing to do with topology in mathematics except the name. Well, the description of a topological insulator does use a tiny bit of topology.
- gmadsen 3y ago
  that is simply not true. They are classified by their topological invariants, which affects their properties.
- civilitty 3y ago
  The topological aspect, very much in the mathematical sense, is that the insulator maintains those properties even when deformed. So when you cut a topological insulator in half to expose the non-conducting inside, that exposed surface becomes conducting again.
  - MikePlacid 3y ago
    That makes me confused even more. Isn’t cutting a non - continuous deformation, that breaks topology?
gmadsen 3y ago
based on the article, they are representing weather patterns on earths surface as a topological insulator. I don't know which class of insulator, but the catagorization of all topological insulators have equivalent classifying spaces of Hamiltonians. Which give you the invariants that you are asking about for deformations of H1 to H2.
- MikePlacid 3y ago
  That makes sense to me, but - neither H1 nor H2 is Earth, they are Hamiltonian spaces. And the statement that puzzles me is: “the Earth can be treated as a topological insulator”. So… I remain puzzled ((

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zornthewise 3y ago

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kergonath 3y ago

That’s a culture difference issue. A topological insulator is a kind of material with specific properties (heavily simplified, that its inside is an electric insulator and its surface is an electric conductor). That’s where the topological aspect comes from. It has nothing to do with topology in mathematics except the name.

staunton 3y ago
> It has nothing to do with topology in mathematics except the name. Well, the description of a topological insulator does use a tiny bit of topology.
gmadsen 3y ago
that is simply not true. They are classified by their topological invariants, which affects their properties.
civilitty 3y ago
The topological aspect, very much in the mathematical sense, is that the insulator maintains those properties even when deformed. So when you cut a topological insulator in half to expose the non-conducting inside, that exposed surface becomes conducting again.
- MikePlacid 3y ago
  That makes me confused even more. Isn’t cutting a non - continuous deformation, that breaks topology?

gmadsen 3y ago

based on the article, they are representing weather patterns on earths surface as a topological insulator. I don't know which class of insulator, but the catagorization of all topological insulators have equivalent classifying spaces of Hamiltonians. Which give you the invariants that you are asking about for deformations of H1 to H2.

MikePlacid 3y ago
That makes sense to me, but - neither H1 nor H2 is Earth, they are Hamiltonian spaces. And the statement that puzzles me is: “the Earth can be treated as a topological insulator”. So… I remain puzzled ((