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In trying to prove Cerf's theorem about homotopies between Morse-functions I ended up thinking about the following problem. For $n>2$, $a= (a_{i,j})\in GL(n-2)$, we define the polynomial map $C_a:\...

For a smooth, real surface $\Sigma$, its bundle of symmetric, bi-linear forms $S^2T\Sigma$ reduced to a $PGL(2,\mathbb{R})$ structure. A similar reduction(with different structure group) can be done ...