Cellular homology groups

Definition 3.38. For an arbitrary CW complex A, the homology groups of the cellular chain complex defined above are called cellular homology groups of A, and are denoted by iJ "(Z 7 .). 

Fortunately, there is another interpretation of the cellular chain groups as certain relative homology groups. The above property of the cellular boundary... 

Again we see that the identity map induces identity maps, and that the composition of two cellular maps induces the composition of induced maps. Theorem 3.41 is best when one uses the alternative definition of cellular homology using the relative homology groups. It will follow in that context from the naturality of the associated long exact sequence of a pair. We postpone the precise argument until Subsection 5.2.2. 

Let X be an arbitrary CW complex. It is easy to see that for every A > 0, the relative homology group Hk X X X) is free abelian, with a basis indexed by the fe-cells of X. Hence, we can use the group as an alternative definition for the cellular chain group The cellular... 

Protein kinase B, or Akt, was discovered as the product of an oncogene of the acutely transforming retrovirus AKT8, causing T-cell lymphomas in mice. It encodes a fusion product of a cellular serine/threonine protein kinase and the viral structural protein Gag. This kinase is similar to both protein kinase Ce (PKCe 73% identity to the catalytic domain) and protein kinase A (PKA 68%). It differs from other protein kinases in that it contains a pleckstrin homology (PH) domain, which allows it to bind to polyphosphoinositide head groups (and also to G-protein fly subunits). To date, three subtypes have been identified a, (3, and y, all of which show a broad tissue distribution. It... 

---