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Hypoelliptic Laplacian and Bott-Chern Cohomology: A Theorem of Riemann-Roch-Grothendieck in Complex Geometry (Progress in Mathematics)
Jean-Michel Bismut
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Description for Hypoelliptic Laplacian and Bott-Chern Cohomology: A Theorem of Riemann-Roch-Grothendieck in Complex Geometry (Progress in Mathematics)
Hardcover. This 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. Series: Progress in Mathematics. Num Pages: 203 pages, biography. BIC Classification: PBPD. Category: (P) Professional & Vocational. Dimension: 242 x 161 x 18. Weight in Grams: 466.
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 ... Read more
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 ... Read more
Product Details
Format
Hardback
Publication date
2013
Publisher
Birkhäuser
Condition
New
Series
Progress in Mathematics
Number of Pages
203
Place of Publication
Basel, Switzerland
ISBN
9783319001272
SKU
V9783319001272
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15
About Jean-Michel Bismut
Jean-Michel Bismut is Professor of Mathematics at Université Paris-Sud (Orsay) and a member of the Académie des Sciences. Starting with a background in probability, he has worked extensively on index theory. With Gillet, Soulé, and Lebeau, he contributed to the proof of a theorem of Riemann–Roch–Grothendieck in Arakelov geometry. More recently, he has developed a theory of the hypoelliptic Laplacian, a ... Read more
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