Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Holonomy (2)
- Analysis (1)
- Arithmetic invariants (1)
- Chaos (1)
- Cohomology (1)
-
- Composed simplicial complexes (1)
- De Rham theorem (1)
- Differential K-theory (1)
- Dirichlet domains (1)
- Entropy (1)
- Fractal (1)
- GNS construction (1)
- Gauge theory (1)
- Gerbes (1)
- Hochschild Complex (1)
- Hyperbolic 3-manifolds (1)
- Hyperbolic surfaces (1)
- Ligeti (1)
- Macfarlane (1)
- Music (1)
- Non abelian (1)
- Parallel Transport (1)
- Piano Concerto (1)
- Polyhedral products (1)
- Principal bundle (1)
- Quaternion algebras (1)
- Real moment-angle complexes (1)
- States on C*-algebras (1)
- Toric topology (1)
- Twisted Chern Character (1)
Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Some 2-Categorical Aspects In Physics, Arthur Parzygnat
Some 2-Categorical Aspects In Physics, Arthur Parzygnat
Dissertations, Theses, and Capstone Projects
2-categories provide a useful transition point between ordinary category theory and infinity-category theory where one can perform concrete computations for applications in physics and at the same time provide rigorous formalism for mathematical structures appearing in physics. We survey three such broad instances. First, we describe two-dimensional algebra as a means of constructing non-abelian parallel transport along surfaces which can be used to describe strings charged under non-abelian gauge groups in string theory. Second, we formalize the notion of convex and cone categories, provide a preliminary categorical definition of entropy, and exhibit several examples. Thirdly, we provide a universal description …
On The Derivative Of 2-Holonomy For A Non-Abelian Gerbe, Cheyne J. Miller
On The Derivative Of 2-Holonomy For A Non-Abelian Gerbe, Cheyne J. Miller
Dissertations, Theses, and Capstone Projects
The local 2-holonomy for a non abelian gerbe with connection is first studied via a local zig-zag Hochschild complex. Next, by locally integrating the cocycle data for our gerbe with connection, and then glueing this data together, an explicit definition is offered for a global version of 2-holonomy. After showing this definition satisfies the desired properties for 2-holonomy, its derivative is calculated whereby the only interior information added is the integration of the 3-curvature. Finally, for the case when the surface being mapped into the manifold is a sphere, the derivative of 2-holonomy is extended to an equivariant closed form …
A Geometric Model Of Twisted Differential K-Theory, Byung Do Park
A Geometric Model Of Twisted Differential K-Theory, Byung Do Park
Dissertations, Theses, and Capstone Projects
We construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. We use smooth U(1)-gerbes with connection as differential twists and twisted vector bundles with connection as cycles. The model we construct satisfies the axioms of Kahle and Valentino, including functoriality, naturality of twists, and the hexagon diagram. We also construct an odd twisted Chern character of a twisted vector bundle with an automorphism. In addition to our geometric model of twisted differential K-theory, we introduce a smooth variant of the Hopkins-Singer model of differential K-theory. We prove that our model is naturally …
The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong
The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong
Dissertations, Theses, and Capstone Projects
This interdisciplinary study explores musical-mathematical analogies in the fourth movement of Ligeti’s Piano Concerto. Its aim is to connect musical analysis with the piece’s mathematical inspiration. For this purpose, the dissertation is divided into two sections. Part I (Chapters 1-2) provides musical and mathematical context, including an explanation of ideas related to Ligeti’s mathematical inspiration. Part II (Chapters 3-5) delves into an analysis of the rhythm, form, melody / motive, and harmony. Appendix A is a reduced score of the entire movement, labeled according to my analysis.
Cohomology Of Certain Polyhedral Product Spaces, Elizabeth A. Vidaurre
Cohomology Of Certain Polyhedral Product Spaces, Elizabeth A. Vidaurre
Dissertations, Theses, and Capstone Projects
The study of torus actions led to the discovery of moment-angle complexes and their generalization, polyhedral product spaces. Polyhedral products are constructed from a simplicial complex. This thesis focuses on computing the cohomology of polyhedral products given by two different classes of simplicial complexes: polyhedral joins (composed simplicial complexes) and $n$-gons. A homological decomposition of a polyhedral product developed by Bahri, Bendersky, Cohen and Gitler is used to derive a formula for the case of polyhedral joins. Moreover, methods from and results by Cai will be used to give a full description of the non-trivial cup products in a real …
Quaternion Algebras And Hyperbolic 3-Manifolds, Joseph Quinn
Quaternion Algebras And Hyperbolic 3-Manifolds, Joseph Quinn
Dissertations, Theses, and Capstone Projects
I use a classical idea of Macfarlane to obtain a complex quaternion model for hyperbolic 3-space and its group of orientation-preserving isometries, analogous to Hamilton’s famous result on Euclidean rotations. I generalize this to quaternion models over number fields for the action of Kleinian groups on hyperbolic 3-space, using arithmetic invariants of the corresponding hyperbolic 3-manifolds. The class of manifolds to which this technique applies includes all cusped arithmetic manifolds and infinitely many commensurability classes of cusped non-arithmetic, compact arithmetic, and compact non-arithmetic manifolds. I obtain analogous results for actions of Fuchsian groups on the hyperbolic plane. I develop new …