No, but mercenary groups often traveled eastward in the service of the Byzantine Emperors. Large-scale military efforts of assistance of that sort across long distances simply didn't occur in the medieval world. There are lots of reasons why, but first and foremost was that there was not a national or supra-national coalition to call for such an event. Even if one had spontaneously formed, in the eleventh century there was no ruler or group of rulers with the bureaucracy necessary to create a long-distance logistical chain to support such an expedition.

It should be emphasized that historians do not see the First Crusade as an effort to help the fledging Byzantine Empire. There is a fair amount of misinformation floating around on the internet over the last few years that has made comparisons between the advances of Islamic forces in the seventh and eleventh centuries with the current refugee crisis or the spread of ISIS with the medieval past. Indeed, strong reporting has shown ISIS openly invites this association, since it actively employs medieval intellectual thought as a basis for establishing what it believes ought to be "tradition." Commentators, particularly on the alt-right, have then drawn corollaries, cited poor history, and meme'd Deus Vult into calls for a new crusade, like the one that saved the Byzantine Empire and repelled the Turks in the eleventh century. Long live Alexios.

It doesn't help that there has been a lot of speculation amongst historians about why Alexios reached out to Urban in 1095. But, before we get to that, lets outline what we know. In March of 1095, an envoy from the Emperor of the Romans arrived in northern Italy to meet with Pope Urban II carrying a letter. The contents of the letter or what was said during the embassy's audience with the Pope, presuming one was offered directly, is not recorded. Communication between these two parties wasn't entirely unusual. They regularly corresponded on matters of religious doctrine and odd bits of diplomatic chatter that has become fodder for historical "what ifs." For example, following Byzantine losses in southern Italy, the Emperor Michael VII had attempted to forge a sort of weird military alliance with the Papacy in 1073 to confront the Norman and Turkish threat. Gregory VII politely declined. All of this is to say that Byzantine Emperors routinely sent representatives westward to Rome in order to secure mercenaries to help with their campaigns. For a variety of reasons we won't get into here, the Byzantine system of land holding made the recruitment of soldiers by the Emperor difficult. Under the Kommeni the army underwent a series of reforms, but this was an ongoing process that began with Alexios and continued under his successors: Alexios needed soldiers now.

The relationship between Urban and Alexios had a certain amount of tension. In 1088/9, Urban had complained in a letter to Alexios concerning the treatment of Latin Christians in Constantinople and the omission of his name and title as "Bishop of Rome" in the liturgy of the mass employed in the Orthodox church. But, despite these diplomatic sparks, Alexios had seen results from an early embassy in 1090 and secured aid in the form of mercenaries from Urban for campaigns in Pecheneg. That campaign proved successful and in 1095 the situation looked even more promising, since the Seljuk Turks of Nicea were struck by internal infighting. Thus, in sending an embassy in 1095, Alexios probably was looking to take advantage of the moment by requesting western mercenaries to support his own troops.

There is, however, an omission here that I haven't mentioned and that some historians make a very big deal out of. Oddly enough, Alexios's principal chroniclers, his daughter Anna and his personal secretary John Zonaras, do not record the diplomatic mission of 1095 to Urban. Certain historians believe that the silence of these historians on what would be such a fateful diplomatic exchange speaks to Alexios's role in manipulating the Pope and, by consequence, the call for the First Crusade. In this view, Alexios is the crusade's principal architect: playing four dimensional chess like Frank Underwood to fan the flames of interfaith conflict for his own ends. While this could be true, it is an argument made from imagination and silence: there is no evidence that I am aware of that gives any insight into Alexios's role behind planning the First Crusade.

Urban's motivations for calling the First Crusade, what inspired his thinking, and what drove knights to take up his call are all entirely different matters, but I hope this explains something of why Alexios would have reached out to Urban and how what Urban responded with was totally out of step with their previous diplomatic exchanges. I hope it also chips away at the idea of Alexios seeking to create a previously unimagined pan-Christian army against his Turkish foes. Alexios disliked and distrusted the European knights who arrived with an army on his doorstep, just as those European knights treated the Byzantines with equal amount of disdain.

I invite any Byzantinists to refine any misunderstandings and add nuance to my narrative of the state of the Byzantine army in the eleventh century; when I read Treadgold's textbook long ago, it was an aging text. For the relationship of Byzantium to western Europe, I strongly recommend beginning with Jonathan Harris, whose Byzantium and the Crusades (2014) is in its second edition. I would be remiss if I didn't also mention Peter Frankopan's The First Crusade: The Call from the East (2012). For the school of thought that sees Alexios Kommenus as the man behind the curtain, here are two examples among others: France, Anna Comnena, the Alexiad and the First Crusade (1984) and Thomas, Anna Commena's Account of the First Crusade (1991)

Could you be a little more specific as to what you mean?