New invariants extracted from the topology of complexifications of real algebraic sets classify algebraic vector bundles over sphere products and obstruct weak algebraic approximation, disproving Kucharz-Kurdyka conjecture.
K -theory and reality
6 Pith papers cite this work, alongside 377 external citations. Polarity classification is still indexing.
6
Pith papers citing it
377
external citations · OpenAlex
verdicts
UNVERDICTED 6representative citing papers
The Galois groupoid of G-spectra is equivalent to the étale fundamental groupoid of the Burnside ring of G.
Hermitian forms on Hilbert spaces arise from the monoid structure of complex conjugation in Z/2-equivariant real linear types within LHoTT, requiring only a negative unit term.
Twisted R-algebra structures on quotients of real ring spectra are built via Thom spectra, enabling real THH computations including for KR/2.
The mod-2 cohomology algebra of moduli stacks of fixed-rank, fixed-degree real vector bundles on type I real algebraic curves is determined by characteristic classes induced from complex Atiyah-Bott classes.
Constructs multi-framed real monopole Floer homology for 3-manifolds with involutions and defines Z-valued invariants for 4-manifolds with involutions.
citing papers explorer
-
Invariants of real affine varieties based on their complexifications
New invariants extracted from the topology of complexifications of real algebraic sets classify algebraic vector bundles over sphere products and obstruct weak algebraic approximation, disproving Kucharz-Kurdyka conjecture.
-
The Galois theory of $G$-spectra and the Burnside ring
The Galois groupoid of G-spectra is equivalent to the étale fundamental groupoid of the Burnside ring of G.
-
Quantum and Reality
Hermitian forms on Hilbert spaces arise from the monoid structure of complex conjugation in Z/2-equivariant real linear types within LHoTT, requiring only a negative unit term.
-
Equivariant twisted $R$-algebras via Thom spectra
Twisted R-algebra structures on quotients of real ring spectra are built via Thom spectra, enabling real THH computations including for KR/2.
-
Cohomology of the Moduli Stacks of Real Vector Bundles on Type I Real Algebraic Curves
The mod-2 cohomology algebra of moduli stacks of fixed-rank, fixed-degree real vector bundles on type I real algebraic curves is determined by characteristic classes induced from complex Atiyah-Bott classes.
-
Multi-framed real monopole Floer theory
Constructs multi-framed real monopole Floer homology for 3-manifolds with involutions and defines Z-valued invariants for 4-manifolds with involutions.