Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a c

Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C∞-schemes with corners'.

If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operatio