Real Seiberg-Witten Floer homotopy types of Seifert 3-manifolds with odd involutions are shown to be equivalent to a suspension of C_+ by the Fukumoto-Furuta w-invariant, yielding eventual periodicity in branched covers of torus knots and linear independence of the 8δ_R^{(k)} invariants.
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Complements of embeddings A^1 into A^3 admit universal abelian K^MW_2-coverings, giving a motivic Alexander-module invariant that detects non-rectifiable algebraic knots.
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Real Floer Homotopy Types and $w$-Invariants
Real Seiberg-Witten Floer homotopy types of Seifert 3-manifolds with odd involutions are shown to be equivalent to a suspension of C_+ by the Fukumoto-Furuta w-invariant, yielding eventual periodicity in branched covers of torus knots and linear independence of the 8δ_R^{(k)} invariants.
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Algebraic Knots and their Universal K^MW_2-Coverings
Complements of embeddings A^1 into A^3 admit universal abelian K^MW_2-coverings, giving a motivic Alexander-module invariant that detects non-rectifiable algebraic knots.
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On Galois categories and condensed contractible schemes
The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.
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Shape theory for condensed anima
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.