As a complement to more scholarly references, you might enjoy this video recording of a delightful interview with Kirby. In the section labeled "The Torus Trick," he gives a description of the trick which I found enlightening both mathematically as well as historically (though it's a bit brief). Some of the surrounding sections of the video contain further interesting information about the state of topology at the time.

As a complement to more scholarly references, you might enjoy this video recording of a delightful interview with Kirby. In the section labeled "The Torus Trick," he describes the process which brought him to discover the trick, which I found both mathematically and historically interesting, though it's a bit brief. Some of the surrounding sections of the video contain further interesting information about the state of topology at the time.