13 votes
Accepted

Possible mistake in Cohen notes "Immersions of manifolds and homotopy theory" (version 27 March 2022)

The statement is false in two ways. First, two immersions might not even be homotopic even though their normal bundles are both, say, trivial. Second, even if $M=\mathbb R^m$, regular homotopy classes ...
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6 votes
Accepted

Stable normal bundle and immersions

This follows from obstruction theory; also see this answer. If $E \to X$ is a rank $r$ real vector bundle over a CW complex $X$, then the obstructions to finding a nowhere-zero section lie in $H^i(X; \...
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