The Farrell-Hsiang method revisited

We present a sufficient condition for groups to satisfy the Farrell-Jones Conjecture in algebraic K-theory and L-theory. The condition is formulated in terms of finite quotients of the group in question and is motivated by work of Farrell-Hsiang.Comment: This version is different from the published version. A number of typos and an incorrect formula for the transfer before Lemma 6.3 pointed out by Holger Reich have been correcte

Coefficients for the Farrell-Jones Conjecture

We introduce the Farrell-Jones Conjecture with coefficients in an additive category with G-action. This is a variant of the Farrell-Jones Conjecture about the algebraic K- or L-Theory of a group ring RG. It allows to treat twisted group rings and crossed product rings. The conjecture with coefficients is stronger than the original conjecture but it has better inheritance properties. Since known proofs using controlled algebra carry over to the set-up with coefficients we obtain new results about the original Farrell-Jones Conjecture. The conjecture with coefficients implies the fibered version of the Farrell-Jones Conjecture.Comment: 21 page

Geography

Jeremiah Farrell\u27s crossword puzzle titled Geography with answer page, which was a contribution to the American Mensa Mind Games

The geometry and combinatorics of Springer fibers

This survey paper describes Springer fibers, which are used in one of the earliest examples of a geometric representation. We will compare and contrast them with Schubert varieties, another family of subvarieties of the flag variety that play an important role in representation theory and combinatorics, but whose geometry is in many respects simpler. The end of the paper describes a way that Springer fibers and Schubert varieties are related, as well as open questions.Comment: 18 page