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Algebraic Topology
Fundamental groups, homology: counting holes with algebra.
មេរៀន
polar form of -1
Advanced
Homology and the Euler characteristic
Counting holes in every dimension with chain complexes.
6 - 12 + 8
Attach a group to a space so that continuous maps become homomorphisms. Then the question "are these two spaces the same shape?" becomes an algebra computation, which is how we know a doughnut is not a sphere.
មេរៀនបន្ថែម
Homotopy
Homology
Consequences
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សំណួរដែលមនុស្សសួរ
What does the fundamental group measure?
Loops in a space up to deformation. In a plane every loop shrinks to a point (trivial group); around a hole a loop can wind n times (the integers).
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