We show that the L 2 -curvature pinching locally conformally flat 3-manifolds can be deformed to space forms through such gradient flow. More precisely, for the suitable small initial energy functional , the gradient flow exists for all times and converges smoothly to space forms as the time ...
\quad Then M^{\alpha} for sufficiently large \alpha are diffeomorphic to graph manifolds. \quad Indeed, there is only one exceptional case, not covered by the theorem above, namely, when M=M^{-}(w, t), and \rho(x, t), for some x \in M, is much larger than the diameter d(t...
connected sum above admits a metric of positive scalar curvature.) Moreover, if the scalar curvature is only nonnegative, then by the strong maximum principle it instantly becomes positive unless the metric is (Ricci-)flat; thus in this case, we need to add to our list the flat manifolds....
Monopoles and Three-manifolds 作者: Kronheimer, Peter/ Mrowka, Tomasz 出版年: 2008-2页数: 810定价: $ 202.27丛书: New Mathematical MonographsISBN: 9780521880220豆瓣评分 评价人数不足 评价: 写笔记 写书评 加入购书单 分享到 推荐 内容简介 ··· Originating with Andreas Floer in the 1980s, Floer...
We describe an algorithm which has enabled us to give a complete list, without repetitions, of all closed oriented irreducible three-manifolds of complexity up to 9. More interestingly, we have actually been able to give a name to each such manifold, by recognizing its canonical decomposition ...
Monopoles and Three-Manifolds || Further developments Morse theory computes the homology groups of a manifold by analysing the critical points and gradient flow of a given function f on the manifold. Floer theory is an analogue of Morse theory for certain infinite-dimensional spaces: specif... P...
G. Massuyeau, Finite-type invariants of three-manifolds and the dimension subgroup problem, preprint (2006), math.GT/0605497, to appear in J. London Math. Soc.G. Massuyeau, Finite-type invariants of three-manifolds and the dimension subgroup problem, J. London Math. Soc. 75 (2007) 791...
universitext(共286册), 这套丛书还有 《An Invitation to Morse Theory》《Algebraic Topology from a Homotopical Viewpoint》《Geometry II》《Intuitive Combinatorial Topology》《Hyperplane Arrangements》 等。 我要写书评 Classical Tesselations and Three-Manifolds的书评 ···(全部 0 条) 当前版本...
L. Rozansky and E. Witten, "Hyper-Kaehler geometry and invariants of three- manifolds," Selecta Math. 3, 401 (1997) [arXiv:hep-th/9612216].L. Rozansky and E. Witten, "Hyper-Kaehler geometry and invariants of three-manifolds," Selecta Math. 3, 401 (1997) [arXiv:hep-th/9612216]....
摘要: A Riemannian manifold has CVC ( ) if its sectional curvatures satisfy sec ≤ε or sec ≥ε pointwise, and if every tangent vector lies in a tangent plane of curvature ε. We present a construction of an infinite-dimensional family of compact CVC ( 1 ) three-manifolds...