Show that \(SL_2(\mathbb {R})\), viewed as the subset \[ \{(a,b,c,d)\mid ad-bc=1\} \] of \(\mathbb {R}^4\), is a manifold.
Question
Math 6510 • Differentiable Manifolds
Fall 1999 • Question 4
Question
Fall 1999 • Question 4
Show that \(SL_2(\mathbb {R})\), viewed as the subset \[ \{(a,b,c,d)\mid ad-bc=1\} \] of \(\mathbb {R}^4\), is a manifold.