TY - JOUR
T1 - Differential KO-theory
T2 - Constructions, computations, and applications
AU - Grady, Daniel
AU - Sati, Hisham
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/6/25
Y1 - 2021/6/25
N2 - We provide several constructions in differential KO-theory. First, we construct a differential refinement of the Aˆ-genus and a pushforward leading to a Riemann-Roch theorem. We set up a differential refinement of the Atiyah-Hirzebruch spectral sequence (AHSS) for differential KO-theory and explicitly identify the differentials, including ones which mix geometric and topological data. We highlight the power of these explicit identifications by providing a characterization of forms in the image of the Pontrjagin character. Along the way, we fill gaps in the literature where K-theory is usually worked out leaving KO-theory essentially untouched. We also illustrate with examples and applications, including higher tangential structures, Adams operations, and a differential Wu formula.
AB - We provide several constructions in differential KO-theory. First, we construct a differential refinement of the Aˆ-genus and a pushforward leading to a Riemann-Roch theorem. We set up a differential refinement of the Atiyah-Hirzebruch spectral sequence (AHSS) for differential KO-theory and explicitly identify the differentials, including ones which mix geometric and topological data. We highlight the power of these explicit identifications by providing a characterization of forms in the image of the Pontrjagin character. Along the way, we fill gaps in the literature where K-theory is usually worked out leaving KO-theory essentially untouched. We also illustrate with examples and applications, including higher tangential structures, Adams operations, and a differential Wu formula.
KW - Adams operations
KW - Atiyah-Hirzebruch spectral sequence
KW - Differential KO-theory
KW - Riemann-Roch theorem
KW - Whitehead tower
KW - Wu formula
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U2 - 10.1016/j.aim.2021.107671
DO - 10.1016/j.aim.2021.107671
M3 - Article
AN - SCOPUS:85103288126
SN - 0001-8708
VL - 384
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 107671
ER -