In the first part of this paper we prove the multiplicativ property of the relative Quillen Chern character. Then we obtain a Riemann-Roch formula between the relative Chern character of the Bott morphism and the relative Thom form.

We give explicit harmonic representatives of Dolbeault cohomology Oeljeklaus-Toma manifolds and show that they are geometrically formal. also Bott-Chern type $(s,1)$ study the Angella-Tomassini inequality.

<p style='text-indent:20px;'>We construct non-vanishing steady solutions to the Euler equations (for some metric) with analytic Bernoulli function in each three-manifold where they can exist: graph manifolds. Using theory of integrable systems, any admissible Morse-Bott be realized as flow. This interpreted an inverse problem Arnold's structure theorem and yields a corollary topological c...

554 NOTICES OF THE AMS VOLUME 53, NUMBER 5 R aoul Bott passed away on December 20, 2005. In a career spanning five decades, he has wrought profound changes on the landscape of geometry and topology. It is a daunting task to improve upon his own reminiscences [B3], [B4], [B1] and commentaries on papers [B5], punctuated as they are by insight, colorful turns of phrases, and amusing anecdotes. Thi...