CW Complexes

Carboplatin (96) is significantly less toxic in the clinic than cisplatin. Most particularly, it is much less nephrotoxic. Use of a bidentate ligand also ensures formation of a cw complex. Its synthesis begins with cis-diammine platinum diiodide (94) which is reacted with silvw sulfate to give cis-diaquodiam mine platinum sulfate (95). This is reacted with the barium salt of 1,1-cyclo-butanedicarboxylic acid to yield carboplatin [23]. 

Fig. 3. Examples of some of the various symmetries possible for Cw complexes.

Kurnakov s test (1893) is generally applicable to cis- and tranj-ammine dihalides. Addition of thiourea (tu, (H2N)2CS) to the cw-complex leads to successive replacement of all the ligands (Figure 3.29) here the lability of the Pt-Cl bond (see section 3.8.9) causes substitution of a chloride. 

Reductive elimination of the organic partners from 12 reproduces the palladium(O) complex [4 3]. The reaction takes place directly from cis-12, and trans-12 reacts after its isomerization to the corresponding cw-complex (Schemes 2-13 and 2-14). The order of reactivity of the palladium(II) species is diaryl- > (alkyl)aryl- > dipropyl- > diethyl- >... 

The complex [Fe(phen)2(CN)2] shows a smaller chemical isomer shift (0-18 mm s at 300 K) than does [Fe(phen)3](C104)2 (0-31 nun s" ) because of the greater 7i-bonding capabilities of the cyanide. The spectrum of so-called /ra 5 -[Fe(phen)2(CN)2] shows Mossbauer parameters identical to those of the cw-complex and from the arguments in Section 7.4 it can be concluded that the difference is not one of m-/ra j-isomerism [47]. 

The reductive elimination of A-B proceeds if A and B are mutually cis. In other words, reductive elimination is possible from cw-complexes. If groups to be eliminated are trans oriented, they must first rearrange to cis. The cw-diethyl complex... 

In the 14-membered ring, folding to give a cw-complex 3.10 is usually only observed with the trans V configuration... 

In nonpolar solvents that do not contain any traces of water, the addition of HX to IrCl(CO)(PPh3)2 leads to the formation of cw-complexes. However, in moist solvents, a mixture of cis- and trans-complQXQS is obtained.152-155,161-163)... 

Section 2.3 is entirely devoted to triangulated spaces. These will be of crucial importance when we study nerves of acyclic categories in Chapter 10, and will also appear in various combinatorial quotient constructions in Chapter 14. Finally, the last section of this chapter considers the general CW complexes. 

In this section we define the most general class of cell complexes that we use, the CW complexes. Roughly speaking, a CW complex is made up of balls of different dimensions, glued to each other, possibly in a fairly complicated manner. 

We shall now give the first definition of a CW complex this one is along the same gluing lines that we have followed several times already. 

A CW complex X is obtained by the following inductive construction of the skeletons ... 

An important property of CW complexes is expressed by the following proposition. 

Proposition 2.52. A compact subspace of a CW complex is contained in a finite subcomplex. 

Corollary 2.53. For each open cell e in a CW complex X, its closure e is contained in finitely many open cells. 

This proves a part of the equivalence of the two definitions of CW complex. Historically, the CW structure was defined intrinsically, as follows. 

Let X be a Hausdorff topological space, and assume that it is represented as a disjoint union of open cells Ca. Then, the pair (X, the collection of the cells a a) is called a CW complex if the following two conditions are satisfied ... 

CW complexes are normal (meaning that disjoint closed subspaces can be encapsulated in disjoint open subspaces) ... 

For example, all the cell spaces, except for the trisps that we have defined up to now are regular CW complexes. Regular trisps are also regular CW complexes. 

There are many representations of the sphere as a CW complex. Two popular ones are as follows ... 

The real projective space RP can be represented as a CW complex with one cell in each dimension from 0 to n. This cell structure is the Z2-quotient, with respect to the antipodal map, of the cell structure on the sphere S , which we described in (l)(b) above. 

The main reason why CW complexes are so handy for concrete computations of homology groups is that it turns out that one can substitute the simplicial chain complex with another, usually much smaller, chain complex, which we now proceed to define. 

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