Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2007 • Question 6

Question

Math 6510 • Differentiable Manifolds Winter 2007 • Question 6

The set \(SL_2(\mathbb {R})\) of \(2\times 2\) matrices with determinant 1 can be viewed as a subset of \(\mathbb {R}^4\) by choosing an ordering of the matrix entries. Show that this set is a submanifold of \(\mathbb {R}^4\) and compute the tangent space at the identity matrix.

Raw LaTeX

The set \(SL_2(\mathbb{R})\) of \(2\times2\) matrices with determinant 1 can be viewed
as a subset of \(\mathbb{R}^4\) by choosing an ordering of the matrix entries. Show that
this set is a submanifold of \(\mathbb{R}^4\) and compute the tangent space at the identity
matrix.

Topic Tags

Fundamental Groups Smooth Manifolds and Embedded Submanifolds Tangent Spaces and Differential Maps