MADISON, Wisconsin — On an oppressively hot August day in downtown Madison, the signs of this famously liberal city’s progressive activism are everywhere. Buildings are draped in pride flags and Black Lives Matter signs are prominently displayed on storefronts. A musty bookstore advertises revolutionary titles and newspaper clippings of rallies against Donald Trump. A fancy restaurant features a graphic of a raised Black fist in its window, with chalk outside on the sidewalk reading “solidarity forever.”

Yet the Green Party, which bills itself as an independent political party that has the best interests of self-described leftists at heart, is nowhere to be found. It has no storefronts, no candidates running for local office, no relationship with the politically active UW-Madison campus, which has almost 50,000 students.

Where it does have purchase is in the nightmares of local Democrats, who are deeply afraid of the effect the third party might have here in November. As one of the seven presidential battleground states, Wisconsin is a critical brick in the so-called Blue Wall, the term for the run of Rust Belt states that are essential to Kamala Harris’ chances of winning the presidency. It’s a deeply divided state that’s become notorious for its razor-thin margins of victory — a place where statewide elections are so close that even tenths of a percentage point matter. Against that backdrop, the Green Party looms very large this year.