Spectral sequences in combinatorial geometry: Cheeses, inscribed sets, and Borsuk–Ulam type theorems
نویسندگان
چکیده
منابع مشابه
Combinatorial geometry of point sets with collinearities
In this thesis we study various combinatorial problems relating to the geometry of point sets in the Euclidean plane. The unifying theme is that all the problems involve point sets that are not in general position, but have some collinearities. As well as giving rise to natural and interesting problems, the study of point sets with collinearities has important connections to other areas of math...
متن کاملAx-Schanuel type theorems and geometry of strongly minimal sets in differentially closed fields
Let (K; +, ·,′ , 0, 1) be a differentially closed field. In this paper we explore the connection between Ax-Schanuel type theorems (predimension inequalities) for a differential equation E(x, y) and the geometry of the set U := {y : E(t, y)∧ y′ 6= 0} where t is an element with t′ = 1. We show that certain types of predimension inequalities imply strong minimality and geometric triviality of U ....
متن کاملRelative volume comparison theorems in Finsler geometry and their applications
We establish some relative volume comparison theorems for extremal volume forms of Finsler manifolds under suitable curvature bounds. As their applications, we obtain some results on curvature and topology of Finsler manifolds. Our results remove the usual assumption on S-curvature that is needed in the literature.
متن کاملSpectral Sequences on Combinatorial Simplicial Complexes
The goal of this paper is twofold. First, we give an elementary introduction to the usage of spectral sequences in the combinatorial setting. Second we list a number of applications. In the first group of applications the simplicial complex is the nerve of a poset; we consider general posets and lattices, as well as partition-type posets. Our last application is of a different nature: the Sn-qu...
متن کاملCombinatorial Integer Labeling Theorems on Finite Sets with Applications1
Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1,±2, · · · ,±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose tw...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2011
ISSN: 0166-8641
DOI: 10.1016/j.topol.2011.06.035