The Woods Hole fixed point theorem is a farreaching extension of the classical Lefschetz fixed point theorem to vector bundles. It has as corollaries a holomorphic Lefschetz formula for complex manifolds and the Weyl character formula for the irreducible representations of a compact Lie group. Apart from its importance in its own right, the Woods Hole fixed point theorem is crucial in the histo...

We prove that, defined with respect to versal flags, the product of two relative Bott–Samelson varieties over a flag bundle is resolution singularities Richardson variety. This result generalizes Brion’s setting. As an application, this gives singularities, modular interpretation, for Brill–Noether variety imposed ramification on twice-marked elliptic curves.

Bott-Samelson varieties were originally defined as desingularizations of Schubert varieties and were used to describe the geometry of Schubert varieties. In particular, the cohomology of some line bundles on Bott-Samelson varieties were used to prove that Schubert varieties are normal, Cohen-Macaulay and with rational singularities (see for example [BK05]). In this paper, we will be interested ...

Abstract Let $$(X,J,\omega )$$ ( X , J ω ) be a compact 2 n -dimensional almost Kähler manifold. We prove primitive decompositions for Bott–Chern and Aeppli harmonic forms in special bidegrees show that...

In this note we use Bott-Borel-Weil theory to compute cohomology of interesting vector bundles on sequences of Grassmannians.

A. Elmendorf has found an error in the approach to Lemmas 2.2 and 2.3 of “A new proof of the Bott periodicity theorem” (Topology and its Applications, 2002, 167–183). There are also errors in the definitions of the maps in Sections 4.2 and 4.5. In this paper we supply corrections to these errors. We also sketch a major simplification of the argument proving real Bott periodicity, unifying the e...

http://dx.doi.org/10.1016/j.jml.2016.04.004 0749-596X/ 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). q This research received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/20072013)/ERC Grant Agreement n.313610 and was supported...

We prove a version for motivic cohomology of Thomason’s theorem on Bott-periodic K-theory, namely, that for a field k containing the nth roots of unity, the mod n motivic cohomology of a smooth k-scheme agrees with mod n étale cohomology, after inverting the element in H(k, Z/n(1)) corresponding to a primitive nth root of unity.