{"paper":{"title":"Massey products in mapping tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Andrei Pajitnov","submitted_at":"2016-10-04T19:37:49Z","abstract_excerpt":"Let $\\phi: M\\to M$ be a diffeomorphism of a $C^\\infty$ compact connected manifold, and $X$ its mapping torus. There is a natural fibration $p:X\\to S^1$, denote by $\\xi\\in H^1(X, \\mathbb{Z})$ the corresponding cohomology class. Let $\\lambda\\in \\mathbb{Z}^*$. Consider the endomorphism $\\phi_k^*$ induced by $\\phi$ in the cohomology of $M$ of degree $k$, and denote by $J_k(\\lambda)$ the maximal size of its Jordan block of eigenvalue $\\lambda$. Define a representation $\\rho_\\lambda : \\pi_1(X)\\to\\mathbb{C}^*$ by $\\rho_\\lambda (g) = \\lambda^{p_*(g)}.$ Let $H^*(X,\\rho_\\lambda)$ be the corresponding tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01136","kind":"arxiv","version":2},"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"}