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Real-oriented homotopy theory and an analogue of the Adams–Novikov spectral sequence

Hu, Po, Kriz, Igor , TITLE = · 2001 · DOI 10.1016/s0040-9383(99)00065-8

4 Pith papers cite this work. Polarity classification is still indexing.

4 Pith papers citing it
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math.AT 3 math.AG 1

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2026 4

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Invariants of real affine varieties based on their complexifications

math.AG · 2026-05-21 · unverdicted · novelty 7.0

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.

Equivariant twisted $R$-algebras via Thom spectra

math.AT · 2026-07-02 · unverdicted · novelty 6.0

Twisted R-algebra structures on quotients of real ring spectra are built via Thom spectra, enabling real THH computations including for KR/2.

Structured Quotients in Real Homotopy Theory

math.AT · 2026-06-24 · unverdicted · novelty 6.0

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.

Structured Real Snaith Equivalences

math.AT · 2026-06-22 · unverdicted · novelty 5.0

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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Showing 4 of 4 citing papers.

  • Invariants of real affine varieties based on their complexifications math.AG · 2026-05-21 · unverdicted · none · ref 22

    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.

  • Equivariant twisted $R$-algebras via Thom spectra math.AT · 2026-07-02 · unverdicted · none · ref 35

    Twisted R-algebra structures on quotients of real ring spectra are built via Thom spectra, enabling real THH computations including for KR/2.

  • Structured Quotients in Real Homotopy Theory math.AT · 2026-06-24 · unverdicted · none · ref 35

    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.

  • Structured Real Snaith Equivalences math.AT · 2026-06-22 · unverdicted · none · ref 28

    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.