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.
Real-oriented homotopy theory and an analogue of the Adams–Novikov spectral sequence
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Twisted R-algebra structures on quotients of real ring spectra are built via Thom spectra, enabling real THH computations including for KR/2.
Authors construct ring involution structures on quotients of Real bordism, orient Lubin-Tate theory via truncated Brown-Peterson spectra, and characterize equivalences after chromatic localization.
Short proof of Real Snaith equivalences via Wilson spaces yields E6 orientations, recovers E2ρ-structure on Real BP, and computes THR(KUR) and THR(MUPR) using a norm-inverted variant via nilpotence.
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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.
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Structured Quotients in Real Homotopy Theory
Authors construct ring involution structures on quotients of Real bordism, orient Lubin-Tate theory via truncated Brown-Peterson spectra, and characterize equivalences after chromatic localization.
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Structured Real Snaith Equivalences
Short proof of Real Snaith equivalences via Wilson spaces yields E6 orientations, recovers E2ρ-structure on Real BP, and computes THR(KUR) and THR(MUPR) using a norm-inverted variant via nilpotence.