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Algebraic Topology
· Problem 2.2.5
Homology — Allen Hatcher
Mathematics — Topology · degree-theory
Problem
Show that any two reflections of
S
n
S^n
S
n
across different
n
n
n
-dimensional hyperplanes are homotopic, in fact homotopic through reflections. [The linear algebra formula for a reflection in terms of inner products may be helpful.]
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