Copied State Sard’s Theorem. Show that any smooth map \(f:\mathrm {SL}_2(\mathbb {R})\to S^4\) is homotopic to a constant map. Raw LaTeX \begin{enumerate} \item[(a)] State Sard's Theorem. \item[(b)] Show that any smooth map \(f:\SL_2(\R)\to S^4\) is homotopic to a constant map. \end{enumerate} Topic Tags Fundamental Groups Homotopy Equivalence, Retracts, and Contractibility Homotopy and Degree on Manifolds Lie Groups and Matrix Lie Groups