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dc.contributor.advisorMichael J. Hopkins.en_US
dc.contributor.authorZakharevich, Inna (Inna Ilana)en_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2012-09-27T15:26:51Z
dc.date.available2012-09-27T15:26:51Z
dc.date.copyright2012en_US
dc.date.issued2012en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/73376
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (p. 83-84).en_US
dc.description.abstractIn 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.statementofresponsibilityby Inna Zakharevich.en_US
dc.format.extent84 p.en_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.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.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleScissors congruence and K-theoryen_US
dc.title.alternativeScissors congruence as K-theoryen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.identifier.oclc809689660en_US


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