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Formatting - also fixed the tags - this is not really about “differential topology” - the smoothness of the linear flow has little to do with the discussion
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Sam Nead
Sam Nead
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Topology of windings ofon the two torus-torus

edited tags
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Hapax
Hapax
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Better formatting; edited tags; edited tags
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Sam Nead
Sam Nead
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Topology of windings of 2-torustwo torus

In short my question is: what can we say about the quotient topology induced by the linear flow on a 2two-torus? I know that an irrational slope leads to a dense winding and hence (if I'm not mistaken) the quotient topology is trivial. But what about the case where the slope is rational? I know orbits are then homeomorphic to S^1$S^1$ but I can't get my head around what the topology of the quotient space looks like.

Thank you.

Topology of windings of 2-torus

In short my question is: what can we say about the quotient topology induced by the linear flow on a 2-torus? I know that an irrational slope leads to a dense winding and hence (if I'm not mistaken) the quotient topology is trivial. But what about the case where the slope is rational? I know orbits are then homeomorphic to S^1 but I can't get my head around what the topology of the quotient space looks like.

Thank you.

Topology of windings of two torus

In short my question is: what can we say about the quotient topology induced by the linear flow on a two-torus? I know that an irrational slope leads to a dense winding and hence (if I'm not mistaken) the quotient topology is trivial. But what about the case where the slope is rational? I know orbits are then homeomorphic to $S^1$ but I can't get my head around what the topology of the quotient space looks like.

Thank you.

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Hapax
Hapax
  • 51
  • 1