Prof. Jon Rogness
In this talk I'll describe some folk theorems -- or really more of a "folk viewpoint" -- describing how many topologists think about chain complexes and their homology groups. Sometimes it can be very fruitful to pretend that chain complexes are topological spaces; many standard constructions with complexes can be described in terms of spheres, disks, the unit interval, mapping cylinders, and so one. The standard definition of homotopic chain maps, for example, seems like a strange algebraic construction which just happens to work out correctly; with this alternate viewpoint, it follows very easily from the same definition we use for spaces.
The talk won't involve any advanced topology, but it would be helpful to be comfortable with terms like "homotopic," "chain complex" and "homology group."
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