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The map from twisted homology to locally finite twisted homology is studied . The effect of the fires was to change profoundly the appearance of the city and to leave the central part bare , except for some reinforced concrete and steel frames and objects such as safes , chimney stacks , and pieces of twisted sheet metal . Lazzo , however , is taking that buffering one step further : He 's keeping Samples away from his own creative folks , the two dozen or so people who pump out all of that twisted programming . This has implications in twisted homology , in particular Milnor fiber homology and higher homotopy groups . Each loop is like a colossal , twisted rainbow - - a 500,000 - mile-long arc that extends into the Sun 's outer atmosphere , or corona , then returns to the surface . As a result , while The Last Laugh does contain spasms of twisted architecture and malevolent shadows , Murnau creates a literal world that is also expressive . Locally finite , twisted homology is discussed and a " nice " basis is presented .