Vector analysis on Sobolev spaces (Q2785906)

If the reviewer had defined a differential structure and then found that one of his differential forms \(\alpha\) had the property \(d^2\alpha \neq 0\), he would have concluded that his differential structure was inconsistent and therefore non-existent. There is a growing school of mathematicians who think that such rigid adherence to logical requirements makes mathematics a dull subject. The author clearly belongs to this new school. He defines \((\infty-p)\) (infinity minus \(p\))-forms on a compact spin manifold and finds that the exterior differential operator is not nilpotent when acting on these forms. Incidentally, in his work an \((\infty-p)\)-form is different from an \((\infty-q)\)-form if \(p\) and \(q\) are different.