Let $f:M\rightarrow W$ be a smooth map between smooth manifolds such that both $M$ and $W$ are compact, connected and oriented. Let $N\subseteq W$ be a closed submanifold. Let us suppose that $$ \#(f,N)=0. $$ Does a smooth map $g:M\rightarrow W$ homotopic to $f$ and such that $g(M)\cap N=\varnothing$ exist?
2026-03-28 12:33:32.1774701212
If the intersection number of two submanifolds is zero, we can deform them so that they are disjoint.
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