A Z2 topological invariant is defined via quantization of the spin-Chern-Simons action for 3D PT- and PC-symmetric class CI band structures.
Classical Chern-Simons on manifolds with spin structure
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abstract
We construct a 2+1 dimensional classical gauge theory on manifolds with spin structure whose action is a refinement of the Atiyah-Patodi- Singer eta-invariant for twisted Dirac operators. We investigate the properties of the Lagrangian field theory for closed, spun 3-manifolds and compact, spun 3-manifolds with boundary where the action is interpreted as a unitary element of a Pfaffian line of twisted Dirac operators. We then investigate the properties of the Hamiltonian field theory over 3-manifolds of the form (R x Y), where Y is a closed, spun 2-manifold. From the action we derive a unitary line bundle with connection over the moduli stack of flat gauge fields on Y.
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UNVERDICTED 2representative citing papers
Smith homomorphisms are defined equivalently via Thom spectrum maps, yielding a fiber sequence whose Anderson dual produces long exact sequences of invertible field theories.
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$\mathbb{Z}_2$ topological invariant in three-dimensional PT- and PC-symmetric class CI band structures
A Z2 topological invariant is defined via quantization of the spin-Chern-Simons action for 3D PT- and PC-symmetric class CI band structures.
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The Smith Fiber Sequence and Invertible Field Theories
Smith homomorphisms are defined equivalently via Thom spectrum maps, yielding a fiber sequence whose Anderson dual produces long exact sequences of invertible field theories.