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A geometric construction of a Calabi quasimorphism on projective space
http://academiccommons.columbia.edu/catalog/ac:188472
Carneiro, Andre R.
http://dx.doi.org/10.7916/D8N29W9T
Fri, 17 May 2013 00:00:00 +0000
We use the rotation numbers defined by ThÃ©ret in [T] to construct a quasimorphism on the universal cover of the Hamiltonian group of CP^n. We also show that this quasimorphism agrees with the Calabi invariant for isotopies that are supported in displaceable subsets of CP^n.
Mathematics
arc2142
Mathematics (Barnard College), Mathematics
Dissertations

Lattice Subdivisions and Tropical Oriented Matroids, Featuring Products of Simplices
http://academiccommons.columbia.edu/catalog/ac:131450
Piechnik, Lindsay C.
http://hdl.handle.net/10022/AC:P:10240
Fri, 29 Apr 2011 00:00:00 +0000
Subdivisions of products of simplices, and their applications, appear across mathematics. In this thesis, they are the tie between two branches of my research: polytopal lattice subdivisions and tropical oriented matroid theory. The first chapter describes desirable combinatorial properties of subdivisions of lattice polytopes, and how they can be used to address algebraic questions. Chapter two discusses tropical hyperplane arrangements and the tropical oriented matroid theory they inspire, paying particular attention to the previously uninvestigated distinction between the generic and nongeneric cases. The focus of chapter three is products of simplices, and their connections and applications to ideas covered in the first two chapters.
Mathematics
lp2149
Mathematics (Barnard College), Mathematics
Dissertations