| 书目名称 | Hypoelliptic Laplacian and Bott–Chern Cohomology | | 副标题 | A Theorem of Riemann | | 编辑 | Jean-Michel Bismut | | 视频video | | | 概述 | Gives an important application of the theory of the hypoelliptic Laplacian in complex algebraic geometry.Provides an introduction to applications of Quillen‘s superconnections in complex geometry with | | 丛书名称 | Progress in Mathematics | | 图书封面 |  | | 描述 | The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann–Roch–Grothendieck for proper submersions. It gives an equality of cohomology classes in Bott–Chern cohomology, which is a refinement for complex manifolds of de Rham cohomology. When the manifolds are Kähler, our main result is known. A proof can be given using the elliptic Hodge theory of the fibres, its deformation via Quillen‘s superconnections, and a version in families of the ‘fantastic cancellations‘ of McKean–Singer in local index theory. In the general case, this approach breaks down because the cancellations do not occur any more. One tool used in the book is a deformation of the Hodge theory of the fibres to a hypoelliptic Hodge theory, in such a way that the relevant cohomological information is preserved, and ‘fantastic cancellations‘ do occur for the deformation. The deformed hypoelliptic Laplacian acts on the total space of the relative tangent bundle of the fibres. While the original hypoelliptic Laplacian discovered by the author can be described in terms of the harmonic oscillator along the tangent bundle and of the geodesic flow, here, t | | 出版日期 | Book 2013 | | 关键词 | Riemann-Roch theorems and Chern characters; analytic torsion; determinants and determinant bundles; hea | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-00128-9 | | isbn_softcover | 978-3-319-03389-1 | | isbn_ebook | 978-3-319-00128-9Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer Basel 2013 |
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发表于 2025-3-21 19:03:05
