A streamlined proof of the convergence of the Taylor tower for embeddings in Rn\mathbb R^n

Manifold calculus of functors has in recent years been successfully used in the study of the topology of various spaces of embeddings of one manifold in another. Given a space of embeddings, the theory produces a Taylor tower whose purpose is to approximate this space in a suitable sense. Central to the story are deep theorems about the convergence of this tower. We provide an exposition of the convergence results in the special case of embeddings into $\mathbb R^n$, which has been the case of primary interest in applications. We try to use as little machinery as possible and give several improvements and restatements of existing arguments used in the proofs of the main results.Comment: Minor changes, final versio

Weighted simple games and the topology of simplicial complexes

We use simplicial complexes to model weighted voting games where certain coalitions are considered unlikely or impossible. Expressions for Banzhaf and Shapley-Shubik power indices for such games in terms of the topology of simplicial complexes are provided. We calculate the indices in several examples of weighted voting games with unfeasible coalitions, including the U.S. Electoral College and the Parliament of Bosnia-Herzegovina.Comment: 23 pages, 5 figures, 4 table