JOURACA_SP_2017
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Hamiltonian Structures of<br />
Spin(7)-Geometry<br />
Kevin Ingles<br />
Many discover the concept of dimension<br />
when first exposed to geometry in high<br />
school. In college students are then exposed<br />
to various concepts in calculus involving<br />
three dimensions. Thus an idea of calculus<br />
in higher dimensions was established. Of<br />
particular interest to me are the dimensions<br />
7 and 8 as they have found applications in<br />
physics. These dimensions include geometries<br />
defined by the G2 and Spin(7) exceptional<br />
holonomy groups, respectively. For<br />
the physicists, there is particular interest in<br />
studying the dynamics of higher dimensional<br />
systems, and a convenient tool of exploration<br />
is the Hamiltonian. In this paper we<br />
defined various Hamiltonian structures on<br />
Spin(7) manifolds and use properties of<br />
Spin(7)-structures to investigate them. We<br />
give some nonexistence results on closed<br />
Spin(7) manifolds that allow for more precise<br />
identifications.<br />
Department of Physics/<br />
Mathematics & Statistics<br />
Physics<br />
Mentor: Dr. Albert Todd<br />
20
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