20 research outputs found
Projective center point and Tverberg theorems
We present projective versions of the center point theorem and Tverberg's
theorem, interpolating between the original and the so-called "dual" center
point and Tverberg theorems.
Furthermore we give a common generalization of these and many other known
(transversal, constraint, dual, and colorful) Tverberg type results in a single
theorem, as well as some essentially new results about partitioning measures in
projective space.Comment: 10 page
Gravitational Chern-Simons terms and black hole entropy. Global aspects
We discuss the topological and global gauge properties of the formula for a
black hole entropy due to a purely gravitational Chern-Simons term. We study
under what topological and geometrical conditions this formula is well-defined.
To this end we have to analyze the global properties of the Chern-Simons term
itself and the quantization of its coupling. We show that in some cases the
coupling quantization may interfere with the well-definiteness of the entropy
formula.Comment: 37 pages, a few comments and references adde