{"paper":{"title":"The Stiefel--Whitney theory of topological insulators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Birgit Wehefritz-Kaufmann, Dan Li, Ralph M. Kaufmann","submitted_at":"2016-04-11T04:54:21Z","abstract_excerpt":"We study the topological band theory of time reversal invariant topological insulators and interpret the topological $\\mathbb{Z}_2$ invariant as an obstruction in terms of Stiefel--Whitney classes. The band structure of a topological insulator defines a Pfaffian line bundle over the momentum space, whose structure group can be reduced to $\\mathbb{Z}_2$. So the topological $\\mathbb{Z}_2$ invariant will be understood by the Stiefel--Whitney theory, which detects the orientability of a principal $\\mathbb{Z}_2$-bundle. Moreover, the relation between weak and strong topological insulators will be u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02792","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}