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A pair of jeans with the leg holes sewn together, i.e. where the legs form one continuous tube, is topologically equivalent to a normal, unmolested pair of jeans. You can't trust topologists.
Normal jeans are homotopic to a cylinder with a point removed. Leg-sewn jeans are homotopic to a torus with a point removed. Both of these can be deformation retracted to a wedge of two circles (roughly: widen the puncture as far as you can).
I miss topology.
Earlier quoted context omitted.
You know the joke about how when you kiss someone, you’re temporarily forming a long tube with an anus at each end? A topologist friend heard that joke and immediately offered a conjecture that that shape is topologically equivalent to the shape you’d get if you connect a mouth to an anus. This got the party discussing if there exists a homeomorphism between making out and eating ass. I agree, you really can’t trust…
It doesn’t exist, because there is no homeomorphism that takes a distance of 0 to non 0, so you can’t change the connections.