Differential KO-theory: Constructions, computations, and applications

Daniel Grady, Hisham Sati

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Article number107671
JournalAdvances in Mathematics
Volume384
DOIs
StatePublished - Jun 25 2021

Keywords

  • Adams operations
  • Atiyah-Hirzebruch spectral sequence
  • Differential KO-theory
  • Riemann-Roch theorem
  • Whitehead tower
  • Wu formula

ASJC Scopus subject areas

  • Mathematics(all)

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