The special linear version of the projective bundle theorem
Abstract
A special linear Grassmann variety SGr(k,n) is the complement to the zero section of the determinant of the tautological vector bundle over Gr(k,n). For a representable ring cohomology theory A() with a special linear orientation and invertible stable Hopf map \eta, including Witt groups and MSL[\eta^{1}], we have A(SGr(2,2n+1))=A(pt)[e]/(e^{2n}), and A(SGr(2,2n)) is a truncated polynomial algebra in two variables over A(pt). A splitting principle for such theories is established. We use the computations for the special linear Grassmann varieties to calculate A(BSL_n) in terms of the homogeneous power series in certain characteristic classes of the tautological bundle.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 arXiv:
 arXiv:1205.6067
 Bibcode:
 2012arXiv1205.6067A
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  KTheory and Homology;
 14F42;
 19G12;
 19G99
 EPrint:
 Some misprints corrected, slightly revised notation