Kee Yuen Lam

The fact that |z|.|w| = |zw| for complex numbers z and w leads to a "sums of squares identity of type (2,2,2)", namely [x1^2 + x2^2] [y1^2 + y2^2] = [x1y1 - x2y2]^2 + [x1y2 + x2y1]^2. Similarly, quaternion and octonion numbers lead to analogous...

The property |z||w| = |zw| of complex numbers leads naturally to the following question concerning sums of squares: in the polynomial ring R = Z[x_1,...,x_r, y_1,... y_s], what is the minimal n such that [(x_1)^2 + ... +(x_r)^2] [(y_1)^2 + ... +(y_s)...

Consider a vector bundle E of rank k over a finite CW complex X. Assume k>dimX for simplicity. If E is not trivial, then it will contain various trivial sub-bundles of maximal rank r. The geometric dimension of E is simply defined to be gd(E)=k-r. It...