Chessboard complexes indomitable

We give a simpler, degree-theoretic proof of the striking new Tverberg type theorem of Blagojević, Ziegler and Matschke. Our method also yields some new examples of “constrained Tverberg theorems” including a simple colored Radonʼs theorem for d + 3 points in R d . This gives us an opportunity to review some of the highlights of this beautiful theory and reexamine the role of chessboard complexes in these and related problems of topological combinatorics.