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- W2949728687 abstract "In this thesis we develop a version of classicalscissors congruence theory from the perspective of algebraicK-theory. Classically, two polytopes in a manifold X are defined tobe scissors congruent if they can be decomposed into finite sets ofpairwise-congruent polytopes. We generalize this notion to anabstract problem: given a set of objects and decomposition andcongruence relations between them, when are two objects in the setscissors congruent? By packaging the scissors congruenceinformation in a Waldhausen category we construct a spectrum whosehomotopy groups include information about the scissors congruenceproblem. We then turn our attention to generalizing constructionsfrom the classical case to these Waldhausen categories, and findconstructions for cofibers, suspensions, and products of scissorscongruence problems." @default.
- W2949728687 created "2019-06-27" @default.
- W2949728687 creator A5012403109 @default.
- W2949728687 date "2012-01-01" @default.
- W2949728687 modified "2023-09-23" @default.
- W2949728687 title "Scissors congruence and K-theory; Scissors congruence as K-theory" @default.
- W2949728687 hasPublicationYear "2012" @default.
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