<<<<<<< ======= Nontrivial spaces
- Question: what happens when we apply the topological operations (suspension, loop-space, etc.) to highly non-trivial spaces?
- Follow-up: What are some of the "nicest" (well-behaved) non-trivial spaces?
- Example: the disjoint union of a sphere with a single point completely changes the mapping space
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A commutator measures how "badly" two terms fail to commute. Commutativity is generally considered a "nice" property, so the commutator tells us how far from this definition of "nice" we are. My general interest is to:
a.) find as many "nice" properties as possible and measure how badly they fail for various objects (test objects)
b.) find natural examples of very nice sets that become very "ugly" with very small modifications