A strong Byzantine Empire based on sustained pre-Manzikert levels would have some interesting repercussions. alh_p is correct that the Ottomans simply replaced the Byzantines in many ways. I think this would particularly remain true in the Balkans. The Byzantines would likely have managed their territories in much the same was as the Ottomans did, and I see Balkan/Hungarian/Austrian politics evolving much along the lines as they did historically, but with the Byzantines playing the role of the Ottomans. The same applies to the French/Hapsburg conflicts, substituting Byzantium as a French ally instead of the Ottomans. However, there are several very important differences:
The Great Schism - By the time of Manzikert, the schism had already occurred. Byzantium staunchly refused to reconcile with Rome until 1453, and at even then it was only a desperation move to keep the Ottomans out of the city. If the Byzantine Empire had remained strong, no such attempt at reconciliation would have occurred. This has a significant impact on religious history. In addition to Islam never penetrating the Balkans (and much of Anatolia), Europe may have evolved very differently if there had been a strong Orthodox power in the east for the last 1000 years. A strong and meddling Orthodox power would likely have impacted the Reformation and perhaps changed the outcome of the Thirty Years War.
Egypt and North Africa - The Byzantines did not control these areas, and likely would not have regained them. Without an Ottoman rise to power, they would have remained independent nations. The Mamluks likely would have survived as an independent Egypt, and without Ottoman support the Barbary Pirates likely would not have posed a serious threat to Europe. This has major implications on the orientation of European politics. The Barbary threat constantly drew attention southwards, and made the Med the center of Europe for many centuries. Without the pirates, more resources and attention would have been focused on strictly European affairs. More wars? Different wars? Different outcomes? Hard to tell. Certainly the Spanish would have been able to bring far more might to bear against the French without the need to always keep an eye on their coast.
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