“Fosse” is here again, back in Japan after its first, hugely successful tour last year mobilized 100,000 fans of the late choreographer-director-actor-dancer Bob Fosse’s astonishing oeuvre.

Directed by Ann Reinking, a main dancer in many of Fosse’s Broadway dance-musicals, such as “Dancin’ ” (1978) and “All That Jazz” (1979), and one of his favorite pupils, this production is a greatest-hits celebration of the groundbreaking technique and sensual style of the chain-smoking American master who died of a heart attack in 1987 at age 60 — by which time he was already a legend in the history of contemporary dance.

The son of a vaudevillian whose trademark was sexual suggestiveness, Fosse was the first director ever to win a Tony for a stage work (“Pippin”), an Oscar for a movie (“Cabaret”) and an Emmy for a television production (“Liza With a Z”) in the same year — 1973.

Throughout his career, he was also known the world over for his masterful dance arrangements of such famous songs as “Bye Bye Blackbird” and “Life Is Just a Bowl of Cherries,” and for hit numbers from his stage productions of “The Pajama Game” (1954), “Sweet Charity” (1972), “Pippin,” “Chicago” (1975) and “Dancin’ ” — with the latter four racking up eight Tonies. As if that weren’t enough for one lifetime, there’s Fosse’s movie version of “Cabaret,” too, and his autobiographical “All That Jazz.”

For Reinking, taking over Fosse’s body of work 10 years after his death must have been a huge challenge, but from the beginning she’s been up to it, winning a best-choreography Tony with her revival of “Chicago” in 1997. Then two years later came “Fosse” — created Broadway-style with her long-term colleagues Richard Maltby Jr. (director/co-conceiver), Chet Walker and Gwen Verdon (artistic advisers), which in 1999 won the Tony for best production.

What Japanese audiences see this time is a new version of “Fosse” with mainly European dancers. Reinking wanted to make a “more adult” production that was more erotic and sensual. This version’s highlight, for instance, is “Take Off With Us” from the movie “All That Jazz,” a number whose climax was cut short in the original Broadway version because, as Reinking puts it, it was “too erotic for those audiences.”

But for audiences here, there is another bonus: 36-year-old actor and dancer Kenya Osumi, well-known for his stage, film and TV work in Japan, who joined the cast at the last moment — so becoming the first Japanese dancer to appear in a Broadway musical.

In addition, Reva Rice — here with her American colleagues as a main dancer in last year’s “Fosse” — is back as a special guest in Japan only.

So this version of “Fosse” fields a dream team, combining European, American and Japanese talents. And without being partial, Osumi shines. His poise and physique stand any comparison with Western dancers, and his fine technique was not lost on audiences, who obviously took him to their heart.

The production itself reminds us just how Fosse’s very sexy dance style has influenced 20th-century dance. Moves such as his trademark “broken doll” (a disjointed style, as the name suggests) and “slow burn” (in which the head and eyes roll very slowly, almost trancelike, like flames from slow-burning paper) are now standards in the dance world.

Instead of relying on orthodox, balletic movements that aim to display body movement, Fosse’s choreography seems more internalized, including movement that appears to shrink the body or turn it inward. Dancers hunching their shoulders or bending their upper bodies, walking like ostriches or moving pigeon-toed around the stage are also among the elements of his revolutionary style and dance theory.

Of course, these dancers sometimes leap and stretch, but even as they do so there is some extra artifice, characteristically Fosse, such as a sideways turn of the head or a crooking of the knee.

It all adds up to a two-act, 2 1/2-hour spectacular — complete with simple and sexy black costumes and the derby (bowler) hats that were a trademark of Fosse’s productions. Though there’s no specific story, and his style is no longer at the frontier of choreography, we can appreciate his artistry as much as ever.

For as a true son of vaudeville, it was Fosse’s great achievement to epitomize the intensity and “cool” of performance’s public face. However, where his art rose above simple entertainment was in its ability to suggest that this sensuality and poise may mask another side — the loneliness of the performer, striving day after day in the spotlights both to please their audiences and (who knows?) even themselves.