{"paper":{"title":"A formula for topology/deformations and its significance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dennis Sullivan, Ruth Lawrence","submitted_at":"2006-10-30T22:03:54Z","abstract_excerpt":"The formula is $\\partial{e}=({\\rm ad}_e)b+\\sum_{i=0}^\\infty{\\frac{B_i}{i!}}({\\rm ad}_e)^i(b-a)\\>,$ with $\\partial{a}+{1\\over2}[a,a] =0$ and $\\partial{b}+{1\\over2}[b,b] =0$, where $a$, $b$ and $e$ in degrees $-1$, $-1$ and 0 are the free generators of a completed free graded Lie algebra $L[a,b,e]$. The coefficients are defined by ${x\\over{e^x-1}}=\\sum_{n=0}^\\infty{B_n\\over{}n!}x^n$. The theorem is that (I) this formula for $\\partial$ on generators extends to a derivation of square zero on $L[a,b,e]$, (II) the formula for $\\partial{e}$ is unique satisfying the first property, once given the form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610949","kind":"arxiv","version":3},"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"}