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 Date: 2007-02-22 11:16:05Mathematics Differential geometry Differentiable manifold Manifold Tangent space Orientability Euclidean space Tangent bundle Atiyah–Singer index theorem Topology Differential topology Mathematical analysis |
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Noncommutative geometry and reality | QUALIFYING EXAMINATION Harvard University Department of Mathematics Tuesday, March 12 (DayLet X be a compact n-dimensional differentiable manifold, and Y ⊂ X a closed submanifold of dimension m. Show that the EDocID: 1uj9Z - View Document |
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![arXiv:0801.4345v2 [math.DG] 26 FebLimit leaves of a CMC lamination are stable William H. Meeks III∗ Joaqu´ın P´erez](https://www.pdfsearch.io/img/6bdde2a05104ca267e366908bae62b68.jpg "arXiv:0801.4345v2 [math.DG] 26 FebLimit leaves of a CMC lamination are stable William H. Meeks III∗ Joaqu´ın P´erez") | arXiv:0801.4345v2 [math.DG] 26 FebLimit leaves of a CMC lamination are stable William H. Meeks III∗ Joaqu´ın P´erezDocID: 1rm2b - View Document |