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What are the ten most fundamental topics in geometric group theory?

This is a pedagogical question prompted by the fact that I am teaching geometric group theory to undergraduates. They are expected to know already know “group theory, euclidean and hyperbolic geometry, fundamental group and covering spaces”.

The number "ten" is in my question to give it a bit of structure. If you think that there are only three fundamental topics (or perhaps, conversely, at least 15) then that's fine with me - I am very interested to hear your opinion. [Since there is no "one correct answer" I've asked the mods to make this question CW.]

The most relevant posts here on MO are perhaps this list of books and this discussion of how to learn about $\mathrm{Out}(F_n)$.

What are the ten most fundamental topics in geometric group theory?

This is a pedagogical question prompted by the fact that I am teaching geometric group theory to undergraduates. They are expected to know already know “group theory, euclidean and hyperbolic geometry, fundamental group and covering spaces”.

The words "ten most" are there to make the question appealing, and to give it a bit of structure. If you think that there are only three "most fundamental" topics (or, conversely, 15 topics whose relative importance are impossible to measure) then that's fine with me - I am very interested to hear your opinion. [Since there is no "one correct answer" I've asked the mods to make this question CW.]

The most relevant posts here on MO are perhaps this list of books and this discussion of how to learn about $\mathrm{Out}(F_n)$.

What are the ten most fundamental topics in geometric group theory?

This is a pedagogical question prompted by the fact that I am teaching geometric group theory to (advanced) undergraduates. The number "ten" is there to give the question a bit of structure. If you think that there are only three fundamental topics (or perhaps, conversely, at least 15) then that's fine with me - I am very interested to hear your opinion. [Since there is no "one correct answer" I've asked the mods to make this question CW.]

The most relevant posts here on MO are perhaps this list of books and this discussion of how to learn about $\mathrm{Out}(F_n)$.

What are the ten most fundamental topics in geometric group theory?

This is a pedagogical question prompted by the fact that I am teaching geometric group theory to undergraduates. They are expected to know already know “group theory, euclidean and hyperbolic geometry, fundamental group and covering spaces”.

The number "ten" is in my question to give it a bit of structure. If you think that there are only three fundamental topics (or perhaps, conversely, at least 15) then that's fine with me - I am very interested to hear your opinion. [Since there is no "one correct answer" I've asked the mods to make this question CW.]

The most relevant posts here on MO are perhaps this list of books and this discussion of how to learn about $\mathrm{Out}(F_n)$.

What are the ten most fundamental topics in geometric group theory?

This is a pedagogical question prompted by the fact that I am teaching geometric group theory to (advanced) undergraduates. The number "ten" is there to give the question a bit of structure. If you think that there are only three fundamental topics (or perhaps, conversely, at least 15) then that's fine with me - I am very interested to hear your opinion. [Since there is no "one correct answer" I've asked the mods to make this question CW.]

What are the ten most fundamental topics in geometric group theory?

This is a pedagogical question prompted by the fact that I am teaching geometric group theory to (advanced) undergraduates. The number "ten" is there to give the question a bit of structure. If you think that there are only three fundamental topics (or perhaps, conversely, at least 15) then that's fine with me - I am very interested to hear your opinion. [Since there is no "one correct answer" I've asked the mods to make this question CW.]

The most relevant posts here on MO are perhaps this list of books and this discussion of how to learn about $\mathrm{Out}(F_n)$.