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Application of semifinite index theory to weak topological phases. (English) Zbl 1442.19016
Wood, David R. (ed.) et al., 2016 MATRIX annals. Cham: Springer. MATRIX Book Ser. 1, 203-227 (2018).
Summary: Recent work by E. Prodan and the second author [Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics. Cham: Springer (2016; Zbl 1342.82002); Rev. Math. Phys. 28, No. 10, Article ID 1650024, 76 p. (2016; Zbl 1358.81130)] showed that weak invariants of topological insulators can be described using Kasparov’s KK-theory. In this note, a complementary description using semifinite index theory is given. This provides an alternative proof of the index formulae for weak complex topological phases using the semifinite local index formula. Real invariants and the bulk-boundary correspondence are also briefly considered.
For the entire collection see [Zbl 1394.00023].

MSC:
19K56 Index theory
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