In algebraic topology, a branch of mathematics, an orientation character on a group π {\displaystyle \pi } is a group homomorphism to the group of two elements ω : π → { ± 1 } {\displaystyle \omega \colon \pi \to \left\{\pm 1\right\}} , where typically π {\displaystyle \pi } is the fundamental group of a manifold. This notion is of particular significance in surgery theory.
In algebraic topology, a branch of mathematics, an orientation character on a group π {\displaystyle \pi } is a group homomorphism to the group of two elements ω : π → { ± 1 } {\displaystyle \omega \colon \pi \to \left\{\pm 1\right\}} , where typically π {\displaystyle \pi } is the fundamental group of a manifold. This notion is of particular significance in surgery theory.
Source: Wikipedia "Orientation character" · CC BY-SA 4.0
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