{"paper":{"title":"Hodge and signature theorems for a family of manifolds with fibration boundary","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Eugenie Hunsicker","submitted_at":"2005-01-07T04:01:17Z","abstract_excerpt":"Let $\\bar{M}$ be a manifold with boundary $Y$ which is the total space of a fibre bundle, and is defined by the vanishing of a boundary defining function, $x$. We prove $L^2$ Hodge and signature theorems for $M$ endowed with a metric of the form $dx^2 + x^{2c} h + k$, where $k$ is the lift to $Y$ of the metric on the base of the fibre bundle, $h$ is a two form on $Y$ which restricts to a metric on each fibre, and $0 \\leq c \\leq 1$. These metrics interpolate between the case when $c=0$, in which case the metric near the boundary is a cylinder, and the case where $c=1$, in which case the metric "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501096","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"}