The execution-style killing of three Kurdish activists in the heart of Paris on Wednesday may threaten peace talks between the Turkish government and Kurdish rebels that have been decades in the making. It immediately evoked memories of past assassinations targeting Kurdish exiles in Europe in the 1980s, and provoked conspiracy theories as complex as any in the Middle East. But for the moment French authorities do not have any specific suspects in what Interior Minister Manuel Valls flatly described as “assassinations.”

The three victims, all women, were discovered in the early hours of Thursday morning in an apartment adjacent to a small information center affiliated with one of several Kurdish activist groups in Paris. All three women had been shot in the head or upper body. And one of the victims, Sakine Cansiz, was identified by other activists as a founder of the Kurdistan Workers Party, or PKK, which has waged guerrilla war and terrorist campaigns against the Turkish state for almost 30 years. The PKK as such has been outlawed in Turkey, the European Union, and the United States as a designated terrorist organization.

After news spread of the slaughter, there were brief protests near the police barricades at the murder scene, then hundreds of mourners gathered at a Kurdish cultural center a few blocks away, trading “what we think but nothing more,” as one put it, about who might have been responsible.

Certainly the timing of the attack appears important. It follows news Wednesday that the government of Turkish Prime Minister Recep Tayyip Erdogan and the Kurdish rebel leader Abdullah Öcalan, imprisoned on an island off the Turkish coast, had reached an unprecedented agreement on a roadmap to end the PKK insurgency.

That conflict, centered in southeastern Turkey, has left an estimated 45,000 dead. But Kurds are spread across parts of Syria, Iran, and Iraq as well, creating a complicated pattern of rival factions, conflicting interests, and shifting alliances. Iraqi Kurds now have a semi-independent state of their own and keep the PKK at arm’s length. But in Syria, the PKK has developed new strongholds in the midst of the civil war, from which it is relatively easy to stage attacks into Turkey. Iran, which has its own restive Kurdish minority, was linked to the murder of Kurdish leaders in France and in Austria in the 1980s. Yet it may have an interest in supporting the PKK’s insurgency against Ankara. “Iran plays this like billiards,” says exiled Iranian Kurdish journalist Khabat Ghorbani Agdham, “it shoots in one direction to hit another.”

Colleagues of Cansiz say they doubted that she would support the peace plan signed onto by Öcalan. But they did not think a schism inside the PKK would lead to such a killing. “The Kurds have no interest in killing each other,” said Leon Edart of the Federation of Kurdish Associations in France. But Edart said it appeared the women had opened the door to let in their attacker or attackers, suggesting they may have been acquainted with them.

Edart told The Daily Beast that colleagues had expected the women to travel to Germany on Wednesday evening, but had been unable to reach them on the phone and grew worried. It seemed no one had the key or the door code for the building at 147 rue La Fayette near the Gare du Nord train station in Paris. Finally, after midnight, seeing that the lights in the apartment were still on, worried friends forced open a door on the bloody scene. According to early reports, two of the women had been shot in the nape of the neck, a third in the chest and stomach; three shell casings are reported to have been discovered by police at the scene.

In addition to Cansiz, who spent 12 years in Turkish prisons and the last 20 years exiled in Europe, another victim of the attack was named as 32-year-old Fidan Doğan, a staffer at the information center and member of the Brussels-based Kurdistan National Congress. The third, Leyla Söylemez, is described as a young activist.

On Thursday morning, French Interior Minister Manuel Valls visited the scene, pledging "to shed light entirely on this completely unacceptable act." Kurdish associations were reportedly calling for a new protest by France’s 150,000-strong Kurdish community at noon on Friday on Paris's symbolic Place de la Bastille.

In Turkey, meanwhile, Kurdish leaders called Thursday for a protest against the women's deaths. And Turkish President Abdullah Gül has called for calm amid concerns the Paris attack could derail the ongoing peace talks. "Unfortunately, some may see the incident as an opportunity. Everybody should come to their senses, and think, and do what is their duty," Gül told media, according to a Dow Jones report.

Indeed, as the investigation led by Paris anti-terrorism authorities gets underway in France, it does appear likely that whoever gunned down three Kurdish women in cold blood in the heart of Paris was no ally to the Turkish-Kurdish peace process. But that is “what people think, nothing more.”