Download A Protogeometric Nature Goddess from Knossos by J.N. Coldstream PDF

Geometry And Topology

By J.N. Coldstream

Show description

Read Online or Download A Protogeometric Nature Goddess from Knossos PDF

Best geometry and topology books

Differential geometry and its applications: proceedings of the 10th International Conference, DGA 2007, Olomouc, Czech Republic, 27-31 August 2007

This quantity comprises invited lectures and chosen examine papers within the fields of classical and smooth differential geometry, worldwide research, and geometric equipment in physics, awarded on the tenth foreign convention on Differential Geometry and its purposes (DGA2007), held in Olomouc, Czech Republic.

Extra resources for A Protogeometric Nature Goddess from Knossos

Example text

Given a non-negative integer m, a standard m-cube m is a copy of the product [0, 1]m in Rm with the usual Euclidean product metric. By composing this inclusion map with an arbitrary isometric embedding of Rm into Rn (for n m) we can think of m-cubes as lying in high dimensional Euclidean spaces. Let 0 k m be an integer. By a k-dimensional face of the standard mcube m we mean a product J m ⊂ m where J = [0, 1] for k of the factors, and J is either {0} or {1} for each of the remaining (m − k) factors.

Suppose J ⊂ J ⊂ R are closed intervals, inf J = inf J , and J \ J contains only one point r of f (0-cells). Then f −1 (J ) is homotopy equivalent to f −1 (J) with the copies of Lk↓ (v, X) (v a vertex with f (v) = r) coned off. A similar statement holds when inf J = inf J is replaced by sup J = sup J and Lk↓ (v, X) by L↑ (v). 6. We refer the reader to [4] for the proof of this theorem. 2. 2 Morse function criterion for free-by-cyclic groups The next proposition gives a local way of telling that a 2-complex is aspherical and has free-by-cyclic fundamental group.

4. K is a pair of 2-simplices meeting along an edge. 5. K is the boundary of a square. ) Now, prove that if K is a simplicial complex, then S(K) is also a simplicial complex. Example (Exercises on flag condition). These exercises require the reader to recall (or look up) the definitions of join, barycentric subdivision and link of a simplex. 1. Prove that the join of two flag complexes is again flag. 2. Prove that the barycentric subdivision of any simplicial complex is flag. 3. Prove that the link (in sense of simplicial complexes) of any simplex in a flag complex is again a flag complex.

Download PDF sample

Rated 4.18 of 5 – based on 11 votes