A bordism computation for K(Z,3) produces two new anomaly classes for U(1) 1-form symmetries: a mixed H₃∧p₁ anomaly in 5d and a Z₂-valued uSq²u anomaly in 7d.
The Pontrjagin Dual of 3-Dimensional Spin Bordism
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abstract
For each space X we define an explicit group, G(X), functorially in X. This group is constructed from the groups of cochains on X. Furthermore, we construct an explicit functorial pairing with values in R/Z between the cochain representatives for elements of G(X) and maps of closed 3-dimensional spin manifolds to X. This pairing induces a pairing between G(X) and the 3-dimensional spin bordism group of X and identifies each with the Pontrjagin dual of the other.
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Stable cohomotopy in codimensions 2 and 3 receives complete algebraic characterizations for CW complexes and bordism interpretations for manifolds, yielding necessary and sufficient conditions for nowhere-vanishing vector bundle sections.
GSO projection consistency in Type II string theory requires the target space X to admit a spin structure (or G-equivariant spin structure for orbifolds), identified by computing the mixed bordism group Ω₃^spin(Bℤ₂ × X) and classifying corresponding theta angles.
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On Quantum Aspects of 1-Form Symmetries II: Bordism, Invertible Phases, and Anomalies
A bordism computation for K(Z,3) produces two new anomaly classes for U(1) 1-form symmetries: a mixed H₃∧p₁ anomaly in 5d and a Z₂-valued uSq²u anomaly in 7d.
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Stable Cohomotopy in Codimensions Two and Three: From Algebraic Characterizations to Bordism-Theoretic Interpretations
Stable cohomotopy in codimensions 2 and 3 receives complete algebraic characterizations for CW complexes and bordism interpretations for manifolds, yielding necessary and sufficient conditions for nowhere-vanishing vector bundle sections.
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What makes spacetime spin in string theory?
GSO projection consistency in Type II string theory requires the target space X to admit a spin structure (or G-equivariant spin structure for orbifolds), identified by computing the mixed bordism group Ω₃^spin(Bℤ₂ × X) and classifying corresponding theta angles.