We show that, if a quaternionic k-dimensional vector bundle l' over the quaternionic projective space Hpn is stably extendible and its non-zero top Pontrjagin class is not zero mod 2, then l' is stably equivalent to the Whitney sum of k quaternionic line bundles provided k S; n.

Michael Klausner is the Nancy and Charles Munger Professor of Business and Professor of Law at Stanford Law School. He can be reached at klausner@ stanford.edu. Jason Hegland is a Fellow and a Director of Securities Litigation Analytics at Stanford Law School. He can be reached at jhegland@ law.stanford.edu. Matthew Goforth is a Research Fellow at Stanford Law School. He can be reached at mgofo...

We show that under the assumption of dynamical symmetry breaking of electro weak interactions by a top quark condensate, motivated by the Top Mode Standard Model, the top quark in this effective theory can be considered then as chiral color soliton (qualiton). This is realized in an effective four-fermion interaction with chiral SU(3)c as well as SU(2)L ⊗ UY (1) symmetry. In the pure top sector...