Skip to main content
MathOverflow

Return to Answer

deleted 11 characters in body
Source Link
Eric Katz
Eric Katz
  • 281
  • 1
  • 6

A good place to start would be to look at covering spaces. A covering space of a topological space X is a space that is locally isomorphic to X but globally unwinds some of the topology. A good reference is Hatcher's Algebraic Topology notes (section 1.3 has what you'd need in the first couple of pages). Sometimes X is the quotient of its covering by a group action. This property is called normality and there is a nice group theoretic condition for it. As a fun exercise, before you even begin, try to find some graphs Y with group actions such that Y/G is the figure 8.

In a certain sense, covering spaces are the "easiest" types of quotients. This is because the action is properly discontinuous. For this reason, the quotient inherits the tropical structure of the original graph. This means For For more exotic group actions, you may want to look at Matthias Herold's preprint: "Tropical orbit spaces and the moduli spaces of elliptic tropical curves." There should be some clues in that paper for how to work with graphs with finite leaves.

A good place to start would be to look at covering spaces. A covering space of a topological space X is a space that is locally isomorphic to X but globally unwinds some of the topology. A good reference is Hatcher's Algebraic Topology notes (section 1.3 has what you'd need in the first couple of pages). Sometimes X is the quotient of its covering by a group action. This property is called normality and there is a nice group theoretic condition for it. As a fun exercise, before you even begin, try to find some graphs Y with group actions such that Y/G is the figure 8.

In a certain sense, covering spaces are the "easiest" types of quotients. This is because the action is properly discontinuous. For this reason, the quotient inherits the tropical structure of the original graph. This means For more exotic group actions, you may want to look at Matthias Herold's preprint: "Tropical orbit spaces and the moduli spaces of elliptic tropical curves." There should be some clues in that paper for how to work with graphs with finite leaves.

A good place to start would be to look at covering spaces. A covering space of a topological space X is a space that is locally isomorphic to X but globally unwinds some of the topology. A good reference is Hatcher's Algebraic Topology notes (section 1.3 has what you'd need in the first couple of pages). Sometimes X is the quotient of its covering by a group action. This property is called normality and there is a nice group theoretic condition for it. As a fun exercise, before you even begin, try to find some graphs Y with group actions such that Y/G is the figure 8.

In a certain sense, covering spaces are the "easiest" types of quotients. This is because the action is properly discontinuous. For this reason, the quotient inherits the tropical structure of the original graph. For more exotic group actions, you may want to look at Matthias Herold's preprint: "Tropical orbit spaces and the moduli spaces of elliptic tropical curves." There should be some clues in that paper for how to work with graphs with finite leaves.

Source Link
Eric Katz
Eric Katz
  • 281
  • 1
  • 6

A good place to start would be to look at covering spaces. A covering space of a topological space X is a space that is locally isomorphic to X but globally unwinds some of the topology. A good reference is Hatcher's Algebraic Topology notes (section 1.3 has what you'd need in the first couple of pages). Sometimes X is the quotient of its covering by a group action. This property is called normality and there is a nice group theoretic condition for it. As a fun exercise, before you even begin, try to find some graphs Y with group actions such that Y/G is the figure 8.

In a certain sense, covering spaces are the "easiest" types of quotients. This is because the action is properly discontinuous. For this reason, the quotient inherits the tropical structure of the original graph. This means For more exotic group actions, you may want to look at Matthias Herold's preprint: "Tropical orbit spaces and the moduli spaces of elliptic tropical curves." There should be some clues in that paper for how to work with graphs with finite leaves.