Stretch fabrics are notoriously hard to process. When your old leggings wear out, they will probably end up in a landfill—even if you try to drop them off for recycling. But a Manhattan startup has developed a new material that could finally make this corner of the apparel industry circular.

“There’s a reason why billions of pounds of textiles ends up in landfills,” says Gangadhar Jogikalmath, cofounder and chief technology officer of the startup called Return to Vendor. “When we dial it down to the microscopic scale,........

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