How Long to Read Hypoelliptic Laplacian and Bott–Chern Cohomology

How Long Does it Take to Read Hypoelliptic Laplacian and Bott–Chern Cohomology?

It takes the average reader 3 hours and 25 minutes to read Hypoelliptic Laplacian and Bott–Chern Cohomology by Jean-Michel Bismut

Assuming a reading speed of 250 words per minute. Learn more

Description

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, the harmonic oscillator has to be replaced by a quartic oscillator. Another idea developed in the book is that while classical elliptic Hodge theory is based on the Hermitian product on forms, the hypoelliptic theory involves a Hermitian pairing which is a mild modification of intersection pairing. Probabilistic considerations play an important role, either as a motivation of some constructions, or in the proofs themselves.

How long is Hypoelliptic Laplacian and Bott–Chern Cohomology?

Hypoelliptic Laplacian and Bott–Chern Cohomology by Jean-Michel Bismut is 203 pages long, and a total of 51,359 words.

This makes it 69% the length of the average book. It also has 63% more words than the average book.

How Long Does it Take to Read Hypoelliptic Laplacian and Bott–Chern Cohomology Aloud?

The average oral reading speed is 183 words per minute. This means it takes 4 hours and 40 minutes to read Hypoelliptic Laplacian and Bott–Chern Cohomology aloud.

What Reading Level is Hypoelliptic Laplacian and Bott–Chern Cohomology?

Hypoelliptic Laplacian and Bott–Chern Cohomology is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Hypoelliptic Laplacian and Bott–Chern Cohomology?

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