Turchin makes the point that only groups can oppress other groups. Even when
we think of a dictator ruling over an entire nation there is usually an ethnic
or religious or economic group that supports that dictator. Without that
group the dictator would be quickly disposed of by his/her own associates.
Therefore cooperation is very important for the birth and establishment of empires.
It takes a cohesive society to create an empire (and not necessarily an advanced, schooled one).
Turchin points out that the Barbarians at the border with the Roman empire
were too fragmented to constitute a serious threat until the Roman empire itself
started promoting a process of confederation of those tribes. It was easier for
the Roman governors to deal with just one barbarian king instead of a multitude
of anarchic tribes. In the long term, those confederations became powerful
enough to overthrow the Roman empire (that in turn was ripped apart by
constant civil warfare).
Empires tend to rise at the frontiers of the declining empire, not within its borders. And that's because the frontier indirectly foster the solidarity among the individuals of a tribe that later becomes the foundation for the strength of the new elite. His best examples are the Frankish kingdom that succeeded the Roman empire and the Arab empire that defeated Persia and Byzantium.
Turchin emphasizes two dual points: "world empires arise where civilizations clash;" "successful empires tend to expand by cultural assimilation" (his words). Somehow he does not integrate the two aspects in a more poignant theory. It looks like there is at work a form of cultural competition, which then selects a winner, who then has to assimilate the loser or in turn fall prey to a new competitor. This is not quite the kind of natural selection that takes place among biological organisms.
However, after Turchin emphasizes that the fortunes of empires are tied to the cohesiveness of their societies the most interesting part of the book should become the analysis of what makes a society more or less cohesive. Unfortunately, that's the book Turchin did not write. He mentions that "rational self-interested agents cannot join together in a functioning society". It seems that humans are genetically programmed to be both rational self-interested agents and to be altruistic agents who build societies, and the "cohesive" society is due to a delicate balance between the two genetic pressures. This is where Turchin gets into sociobiology, showing that cultural evolution works faster than genetic evolution. It was cultural evolution that led humans to create the abstraction of "nation". Everything else in the book is basically a corollary of this much more interesting and convincing theory.
After all, Turchin is a biologist, not a historian. One quickly realizes that his forte is the theory of cooperation, of which the history of empires is just an instance.
Turchin spends a lot of time detailing the fortunes of the French and the British. From their cycles he identifies some general laws. When the rich get richer and the poor get poorer, when inequality grows, interclass cohesion decreases, causing a crisis that may lead to the collapse of the empire. Most empire collapse not because of external aggression but for internal reasons.
He then analyzes the Roman empire, but this is the weakest part of the book. His analysis of the "cycles" is too biased and superficial to be credible. Even worse when he analyzes Italy: if there is one country that proves how counterproductive cooperation can be, that's Italy. Every Italian can tell him that southern Italians have a much stronger bond of cooperation, at all levels, whereas northern Italy is a decadent individualistic society. And yet it is northern Italy that prospers. That is a good example of the many factors that Turchin has ignored in his analyses: southern Italy was ruled by the Spanish for a long time, and is very similar to the other former Spanish colonies in South America, whereas northern Italy was ruled by Germans and Austrians. It does make a difference. Turchin seems to ignore that the gap between northern and southern Italy dates from the beginning of the Italian state (the "questione meridionale").