Sylvester Stallone's First Public Appearance Since Jennifer's Divorce Filing

Sylvester Stallone is still showing up for work, and putting on a face that seems to hide the fact his wife just pulled the trigger on ending their 25 years of marriage.

Sly surprised a bunch of excited fans Thursday at a special screening for his new movie "Samaritan" ... popping up at the AMC Empire 25 theater in New York. Some folks whipped out their cameras to snap the moment, while others clapped and greeted him with smiles.

And, despite it being a difficult time, he seemed to be in pretty good spirits. At one point he grabbed the mic and gave a guy in the audience a warm embrace.

As we reported ... his now-estranged wife Jennifer Flavin filed for divorce a week ago, and in the docs, she claims he's been moving around marital assets to hide them from her and her attorneys -- although Sly denies that.

There's been a lot of back and forth about what might have caused the divorce -- much of it centering on Sly's new Rottweiler, Dwight, which Stallone got tatted on his shoulder ... OVER Jennifer's face!

While sources connected to Sly said an argument about the dog triggered the divorce ... Sly himself tells us that wasn't it.

He says he and Jennifer "just went in different directions," and adds he was totally caught off guard by her filing divorce papers.

Interestingly, though, Jennifer was out in WeHo in early August, and wasn't wearing her wedding ring.