The special linear version of the projective bundle theorem
Algebraic Geometry
2019-02-20 v3 K-Theory and Homology
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.
Cite
@article{arxiv.1205.6067,
title = {The special linear version of the projective bundle theorem},
author = {Alexey Ananyevskiy},
journal= {arXiv preprint arXiv:1205.6067},
year = {2019}
}
Comments
Some misprints corrected, slightly revised notation