PreprintarXiv licencearXiv
The real Betti realization of very effective Hermitian K-theory
Abstract
Real Betti realization is a symmetric monoidal functor from the category of motivic spectra to that of topological spectra, extending the functor that associates to a scheme over ℝ the space of its real points. In this article, we identify the ℰ1-ring structure on the real realization of ko, the very effective cover of Hermitian K-theory KO, by an explicit 2-local fracture square, as being equivalent to L(ℝ)≥ 0, the connective L-theory spectrum of ℝ. Along the way, we also compute the real realization of other motivic ring spectra: motivic cohomology Hℤ and Hℤ/2, the variant Hℤ̃, KO, the very effective cover kgl of algebraic K-theory KGL.
Related
- Real-analytic realization of universal Teichmüller space via complex-structures on H1/2
- Stable and effective restarting of the SS--RR and SS--RRR methods for computing partial eigenpairs of Hermitian matrices
- Hermitian K-theory for stable ∞-categories III: Grothendieck--Witt groups of rings
- Invariant almost Hermitian structures on the maximal real flag manifold of type 𝒜3
- Hermitian manifolds with constant holomorphic sectional curvature or real bisectional curvature
BibTeX
@misc{bannwart2026real,
title = {{The real Betti realization of very effective Hermitian K-theory}},
author = {Julie Bannwart},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20688},
eprint = {2610.20688},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20688},
}
RIS
TY - UNPB
TI - The real Betti realization of very effective Hermitian K-theory
AU - Julie Bannwart
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20688
UR - https://arxiv.org/abs/2610.20688
AB - Real Betti realization is a symmetric monoidal functor from the category of motivic spectra to that of topological spectra, extending the functor that associates to a scheme over ℝ the space of its real points. In this article, we identify the ℰ_1-ring structure on the real realization of ko, the very effective cover of Hermitian K-theory KO, by an explicit 2-local fracture square, as being equivalent to L(ℝ)_≥ 0, the connective L-theory spectrum of ℝ. Along the way, we also compute the real realization of other motivic ring spectra: motivic cohomology Hℤ and Hℤ/2, the variant Hℤ̃, KO, the very effective cover kgl of algebraic K-theory KGL.
ER -