NEW YORK — ABBA sold hundreds of millions of records but they would have been even bigger if they’d paid more attention to the United States. Benny, Björn, Agnetha and Anni-Frid at some point decided they were happy with being the rich dancing queens of Europe and that the tough Stateside nut was just not worth the work to crack. So in the U.S., they were widely seen as a Swedish novelty act, a fad band.

Even the arrival on Broadway of “Mamma Mia!” in 2001 didn’t immediately change that. The show went cautiously to Toronto (ABBA was bigger in Canada) after London for its North American premiere. New York still worried everybody. No reason. It ran on Broadway for 14 years.

Almost a quarter century later, anyone sitting in the Winter Gardens Theatre, or merely reading the boffo grosses of the musical during the preview performances these last few weeks, can see that U.S. audiences are as hungry as ever for “Mamma Mia!,” thanks in part to the movies and maybe the uptick in vinyl and disco nostalgia. All that the producers did this summer was stick the touring production on Broadway to fill an empty theater. It’s the same diminutive set I saw in Chicago, the cool jetty that arrived at the show’s climax got cut years ago and has not returned. Why waste the money?

For those of us who’ve seen that tour half a dozen times, the only surprise is the addition of more live musicians for Broadway, union minimums being a helpful thing in this case. Actual acoustic sounds have replaced some pre-programmed tracks. Awesome! Benny Andersson’s synth work on the Yamaha GX1 and the Moog Polymoog is legendary but “Mamma Mia” combined the original sound with Martin Koch’s clever theatrical arrangements, and it needs lots of humans in the pit.

Happily, that touring cast starred Christine Sherrill as Donna, a star who lacks only name recognition. Sherrill’s massive but vulnerable belt is ideally matched for this material. She’s the best Donna of all time, in my book. Never has a Donna better nailed “The Winner Takes It All,” the show’s brilliant idea for its 11 o’clock number, rehabbing a tragic break-up song that had been rendered weirdly up-tempo in ABBA’s original recording. The rest of the cast is just fine; the oldsters give the material respect while having fun and the kids all seem delighted just to be there. Doing this.

I remember vividly seeing “Mamma Mia!” at London’s Prince Edward Theatre just prior to its opening. People went berserk with delight. The whole concept of a jukebox musical — with an original story that included songs people already knew backwards, used in a fresh storytelling context — was unknown back then and people giggled with excitement as they wondered how, say, “Does Your Mother Know” would be used since the order of the songs was hidden in the program. (With a clever gender switch to avoid any creepiness.)

Back in 1999, the all-female team of writer Catherine Johnson, producer Judy Craymer and director Phyllida Lloyd crafted a brilliant ABBA delivery mechanism, nothing more, nothing less — a simple story about a single hippy mom (British in the U.K., Irish-American in the U.S.) who had slept with at least three guys on the beach in Greece and later had a daughter, Sophie (Amy Weaver), who was getting married at her mum’s taverna and invited all three of her potential dad candidates to the nuptials.

Add in two sidekicks for Donna (Jalynn Steele and Carly Sakolove) and two for Sophie (Haley Wright and Lena Owens) and you had a story that understood sooner than anyone else that emotional mother-and-daughter stories are a goldmine in musical theater, because that is who likes to go. “Mamma Mia!” has the youth POV (well, it did) and also lots of songs of parental regret (“Slipping Through My Fingers” and so on). I can’t overstate my respect for the show; it’s a masterpiece of its populist kind, much imitated but never equalled.

Sure, the chronology doesn’t make sense any more. If the “dot dot dot” shenanigans were happening in 1979, as they say, Donna would be 70 now, which she’s clearly not. But then maybe “Mamma Mia!” is still happening in 1999, given that no one has phones or taverna websites or knows much about DNA tests. But no book refresh was forthcoming; “Mamma Mia!” remains timeless, stuck in the eternal ABBA timewarp, much like the group’s A.I. avatars who entertain in London, cheating aging and mortality.

The big takeaway for me is that even as the U.S. underestimated this band, so Broadway underestimated this brand. It’s a one of a kind. Just watch how many people will come and have fun. Limited run? We’ll see.

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At the Winter Garden Theatre, 1634 Broadway, New York; mammamiabway.com

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