Bosonic beyond-cohomology SPT phases are governed by a mod-3 Steenrod-power differential, and a new 6+1-dimensional Z3×Z3 Dijkgraaf-Witten phase is nontrivial on simplicial complexes but trivial on manifolds.
Hanke, Bordism of elementary abelian groups via inessential brown–peterson homology
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Bosonic SPT and invertible phases and its relation to Steenrod's problem
Bosonic beyond-cohomology SPT phases are governed by a mod-3 Steenrod-power differential, and a new 6+1-dimensional Z3×Z3 Dijkgraaf-Witten phase is nontrivial on simplicial complexes but trivial on manifolds.