Critical values of Fredholm maps

Church, P. T.; Timourian, J. G.

doi:10.1090/S0002-9939-1988-0964885-7

Critical values of Fredholm maps
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by P. T. Church and J. G. Timourian PDF

Proc. Amer. Math. Soc. 104 (1988), 993-998 Request permission

Abstract:

For a ${C^r}$ Fredholm map $A:X \to Y$, let ${T_k}\left ( A \right )$ be the set of $x \in X$ such that codim Range $DA\left ( x \right ) \geq k$. The homotopy of $Y - A\left ( {{T_k}\left ( A \right )} \right )$ is related to that of $Y$, examples are given, and a factorization result is proved.

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