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Scissors congruence and K-theory

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dc.contributor.advisor Michael J. Hopkins. en_US Zakharevich, Inna (Inna Ilana) en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2012-09-27T15:26:51Z 2012-09-27T15:26:51Z 2012 en_US 2012 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. en_US
dc.description Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 83-84). en_US
dc.description.abstract In this thesis we develop a version of classical scissors congruence theory from the perspective of algebraic K-theory. Classically, two polytopes in a manifold X are defined to be scissors congruent if they can be decomposed into finite sets of pairwise-congruent polytopes. We generalize this notion to an abstract problem: given a set of objects and decomposition and congruence relations between them, when are two objects in the set scissors congruent? By packaging the scissors congruence information in a Waldhausen category we construct a spectrum whose homotopy groups include information about the scissors congruence problem. We then turn our attention to generalizing constructions from the classical case to these Waldhausen categories, and find constructions for cofibers, suspensions, and products of scissors congruence problems. en_US
dc.description.statementofresponsibility by Inna Zakharevich. en_US
dc.format.extent 84 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Mathematics. en_US
dc.title Scissors congruence and K-theory en_US
dc.title.alternative Scissors congruence as K-theory en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 809689660 en_US

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