I read in some books that have the notation $\pi_1(X)=0$ to mean $X$ has trivial fundamental group.
My question is why 0 and not 1, i.e. $\pi_1(X)=1$?
Is this a case of additive notation versus multiplicative notation?
Thanks!
2026-03-30 16:02:56.1774886576
Trivial Fundamental Group Notation (1 or 0)
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I see this as an additive/multiplicative notation issue, exactly as you say. It's like when one talks about exact sequences of abelian groups or modules, one often writes $$ 0 \to A \to B \to C \to 0 $$ whereas one may more likely write $$ 1 \to X \to Y \to Z \to 1 $$ for an exact sequence in the category of all groups.