Standard

The special linear version of the projective bundle theorem. / Ananyevskiy, A.

In: Compositio Mathematica, Vol. 151, No. 3, 2015, p. 461-501.

Research output: Contribution to journal › Article › peer-review

Harvard

Ananyevskiy, A 2015, 'The special linear version of the projective bundle theorem', Compositio Mathematica, vol. 151, no. 3, pp. 461-501. https://doi.org/10.1112/S0010437X14007702

APA

Ananyevskiy, A. (2015). The special linear version of the projective bundle theorem. Compositio Mathematica, 151(3), 461-501. https://doi.org/10.1112/S0010437X14007702

Vancouver

Ananyevskiy A. The special linear version of the projective bundle theorem. Compositio Mathematica. 2015;151(3):461-501. https://doi.org/10.1112/S0010437X14007702

Author

Ananyevskiy, A. / The special linear version of the projective bundle theorem. In: Compositio Mathematica. 2015 ; Vol. 151, No. 3. pp. 461-501.

BibTeX

@article{f60a396801db489eaf4125035ab0b715,
title = "The special linear version of the projective bundle theorem",
abstract = "{\textcopyright} The Author 2014. 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 an SL-oriented representable ring cohomology theory A∗(-) with invertible stable Hopf map η, including Witt groups and MSLη∗,∗, we have A∗(SGr(2, 2n + 1)) ≅ A∗(pt)[e]/(e2n), and A∗(SGr(k, n)) is a truncated polynomial algebra over A∗(pt) whenever k(n - k) is even. A splitting principle for such theories is established. Using the computations for the special linear Grassmann varieties, we obtain a description of A∗(BSLn) in terms of homogeneous power series in certain characteristic classes of tautological bundles.",
author = "A. Ananyevskiy",
year = "2015",
doi = "10.1112/S0010437X14007702",
language = "English",
volume = "151",
pages = "461--501",
journal = "Compositio Mathematica",
issn = "0010-437X",
publisher = "Cambridge University Press",
number = "3",

}

RIS

TY - JOUR

T1 - The special linear version of the projective bundle theorem

AU - Ananyevskiy, A.

PY - 2015

Y1 - 2015

N2 - © The Author 2014. 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 an SL-oriented representable ring cohomology theory A∗(-) with invertible stable Hopf map η, including Witt groups and MSLη∗,∗, we have A∗(SGr(2, 2n + 1)) ≅ A∗(pt)[e]/(e2n), and A∗(SGr(k, n)) is a truncated polynomial algebra over A∗(pt) whenever k(n - k) is even. A splitting principle for such theories is established. Using the computations for the special linear Grassmann varieties, we obtain a description of A∗(BSLn) in terms of homogeneous power series in certain characteristic classes of tautological bundles.

AB - © The Author 2014. 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 an SL-oriented representable ring cohomology theory A∗(-) with invertible stable Hopf map η, including Witt groups and MSLη∗,∗, we have A∗(SGr(2, 2n + 1)) ≅ A∗(pt)[e]/(e2n), and A∗(SGr(k, n)) is a truncated polynomial algebra over A∗(pt) whenever k(n - k) is even. A splitting principle for such theories is established. Using the computations for the special linear Grassmann varieties, we obtain a description of A∗(BSLn) in terms of homogeneous power series in certain characteristic classes of tautological bundles.

U2 - 10.1112/S0010437X14007702

DO - 10.1112/S0010437X14007702

M3 - Article

VL - 151

SP - 461

EP - 501

JO - Compositio Mathematica

JF - Compositio Mathematica

SN - 0010-437X

IS - 3

ER -

ID: 3992689