The Edge of Heaven, 15

Context can make or break a film. The Edge of Heaven, by the Turkish-German director Fatih Akin, drew the short straw in competition in Cannes last year. Among a vintage stack of entries including Zodiac, 4 Months, 3 Weeks ... and Silent Light, Akin's thoughtful, somewhat novelistic drama was admired by some, discussed by few. Now Akin's film arrives in Britain during one of the release schedule's several silly seasons: in the week of Be Kind Rewind and the woefully flimsy My Blueberry Nights, The Edge of Heaven comes into its own as the substantial offering that it is.

Cannes wasn't entirely unkind to The Edge of Heaven: it did win the screenwriting award. Indeed, you could come away from the film thinking it was primarily a clever feat of script construction. But it's simply a detached, rather undemonstrative film – certainly compared with the one that made Akin's name, the 2004 Berlin winner Head-On, a tale of amour fou among ferociously charismatic outsiders. Its follow-up marks a neat shift of register, from Head-On's raging oratorio to pensive fugue.

The Edge of Heaven is divided into three parts: two introducing separate sets of characters, both announcing in their titles that two people are fated to die, while the third, entitled "From the Other Side" (also the film's German title), threads the stories together.

Akin's narrative is a meticulously woven fabric of accidents and chance encounters – and, just as importantly, missed encounters. In Bremen, Ali (Tuncel Kurtiz), an elderly Turkish man, takes a fancy to prostitute Yeter (Nursel Kose) and proposes a deal: that she move in and sleep with him on an exclusive basis. Menaced by two Muslim hardliners who warn her to change her ways, Yeter accepts Ali's offer, but things don't go rosily.

Ali's son Nejat (Baki Davrak), who lectures on German literature, goes to Istanbul, looking for Yeter's missing daughter Ayten (Nurgul Yesilcay). He doesn't find her, but we do, in part two: she's a radical activist on the run. Arriving in Germany to look for her mother, she meets Lotte (Patrycia Ziolkowska), a young student: the two women become lovers, to the dismay of Lotte's mother Susanne (Hanna Schygulla, Fassbinder's former muse), who once had radical leanings, but has now opted for a quiet life and unquestioning faith in governments. Turkey, Susanne argues, is about to enter the European Union: how bad can things really be there for a dissident like Ayten?

In fact, things are pretty bad one way or another in The Edge of Heaven: if tangled fate doesn't mess things up for people, the authorities, in Germany and Turkey alike, certainly will. Yet this is really an optimistic film, suggesting that it's the crossing of individuals' paths that offers hope for the world: it's all down to people's readiness to make exchanges, take generous risks, seize the moment.

Akin's drama is one of those intricate multi-stranders that have become the rage in recent years; perhaps it's no accident that the closing credits include thanks to Mexican screenwriter Guillermo Arriaga, who perfected this line of construction in his films with director Alejandro Gonzalez Inarritu.

But Akin's is a much more astute achievement than Inarritu's recent Babel. Where that film painted a fuzzy, we-are-the-world picture of universal interconnectedness, Akin sets his entanglements against concrete politics: globalisation, migration, the decline of the Left, the specific cultural and economic traffic between Germany and Turkey.

You could object that there are no real characters here, that everyone flatly represents a particular social conflict: the bourgeois German daughter embracing Turkish radicalism, the Turkish academic defining his identity in terms of German high culture .... But I don't think Akin primarily wants us to feel deeply for flesh-and-blood people – not in the way we were consumed by the traumatised passions of the couple in Head-On. In its thoughtful, deliberate pace and low-key acting, The Edge of Heaven feels like a mathematical demonstration of how the world (at least the world of this story) works.

Nor does Akin give his contrivances the metaphysical spin of Krzysztof Kieslowski's Three Colours trilogy: he doesn't seek to make us shudder at frissons of the uncanny. He coolly announces that he's manipulating his repetitions and symmetries: a coffin arrives in Turkey, gliding down the ramp of a plane; later, another rolls up a ramp, bound for Germany. This transparency removes any hint of mystification. If Akin depicts a world of mirrorings and crossings, it's because he's interested in the theme of exchange, of crossed frontiers, both as an abstraction and a political reality.

The acting is sensitive, unflashy: the film is that rarity, a genuinely democratic ensemble piece. Still, the story's weight can't help resting finally with Schygulla's character, whose taking stock more or less binds and gives meaning to the fates of the others. Akin leaves us a minor-key open ending: a long take of a character sitting on a beach, musing as he waits for someone else to draw into view. Musing on what? It's our guess.

This elegant, complex drama builds its virtuoso layerings, but then grants us the intelligence to think about their real-world implications – to discern the pattern beyond the pattern. You'll come out thinking, rather than (as in Head-On) reeling. For that, Akin's modest achievement – modest in the best sense – deserves your attention.