{"paper":{"title":"Geometry of determinants of elliptic operators","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"hep-th","authors_text":"Maxim Kontsevich, Simeon Vishik","submitted_at":"1994-06-21T16:29:17Z","abstract_excerpt":"This paper is essentially a short version of hep-th/9404046. We compute multiplicative anomaly det(AB)/(detA detB) =F(A,B) for elliptic pseudo-differential operators (PDOs) A, B on a closed manifold M in terms of their symbols. We prove that F(A,B)=1 for elliptic differential operators close to positive-definite ones on an odd-dimensional M. For such M we introduce a holomorphic determinant. Its monodromy lies in a finite group of roots of unity.\n  In general case, we relate the multiplicative anomaly with a central extension of the group of elliptic symbols and with an invariant quadratic for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9406140","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"}