On the Cobordism Classification of Symmetry Protected Topological Phases

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)


In the framework of Atiyah’s axioms of topological quantum field theory with unitarity, we give a direct proof of the fact that symmetry protected topological phases without Hall effects are classified by cobordism invariants. We first show that the partition functions of those theories are cobordism invariants after a tuning of the Euler term. Conversely, for a given cobordism invariant, we construct a unitary topological field theory whose partition function is given by the cobordism invariant, assuming that a certain bordism group is finitely generated. Two theories having the same cobordism invariant partition functions are isomorphic.

Original languageEnglish
Pages (from-to)1121-1173
Number of pages53
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - 2019 Jun 1


Dive into the research topics of 'On the Cobordism Classification of Symmetry Protected Topological Phases'. Together they form a unique fingerprint.

Cite this