Hjem

Preliminaries.- 1 Simplicial Complexes:
1.1 Topological spaces;
1.2 Homotopy equivalence and homotopy;
1.3 Geometric simplicial complexes;
1.4 Triangulations;
1.5 Abstract simplicial complexes;
1.6 Dimension of geometric realizations;
1.7 Simplicial complexes and posets.- 2 The Borsuk-Ulam Theorem:
2.1 The Borsuk-Ulam theorem in various guises;
2.2 A geometric proof;
2.3 A discrete version: Tucker's lemma;
2.4 Another proof of Tucker's lemma.- 3 Direct Applications of Borsuk--Ulam:
3.1 The ham sandwich theorem;
3.2 On multicolored partitions and necklaces;
3.3 Kneser's conjecture;
3.4 More general Kneser graphs: Dolnikov's theorem;
3.5 Gale's lemma and Schrijver's theorem.- 4 A Topological Interlude:
4.1 Quotient spaces;
4.2 Joins (and products);
4.3 k-connectedness;
4.4 Recipes for showing k-connectedness;
4.5 Cell complexes.- 5 Z_2-Maps and Nonembeddability:
5.1 Nonembeddability theorems: An introduction;
5.2 Z_2-spaces and Z_2-maps;
5.3 The Z_2-index;
5.4 Deleted products good
...;
5.5
... deleted joins better;
5.6 Bier spheres and the Van Kampen-Flores theorem;
5.7 Sarkaria's inequality;
5.8 Nonembeddability and Kneser colorings;
5.9 A general lower bound for the chromatic number.- 6 Multiple Points of Coincidence:
6.1 G-spaces;
6.2 E_nG spaces and the G-index;
6.3 Deleted joins and deleted products;
6.4 Necklace for many thieves;
6.5 The topological Tverberg theorem;
6.6 Many Tverberg partitions;
6.7 Z_p-index, Kneser colorings, and p-fold points;
6.8 The colored Tverberg theorem.- A Quick Summary.- Hints to Selected Exercises.- Bibliography.- Index.