Scissors congruence and K-theory
Name
809689660-MIT.pdf
Description
Full printable version
Size
4.81 MB
Format
Adobe PDF
Checksum (MD5)
73d0621ad9ac9a686379195d191e972d
Author(s)
Zakharevich, Inna (Inna Ilana)
Advisor(s)
Michael J. Hopkins.
Alternative Title
Scissors congruence as K-theory
Date Issued
2012
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 83-84).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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