Graduation Year
2000
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Weiqing Gu
Reader 2
Adolfo Rumbos (Pomona)
Abstract
In the further development of the string theory, one needs to understand 3 or 4-dimensional volume minimizing subvarieties in 7 or 8-dimensional manifolds. As one example, one would like to understand 4-dimensional volume minimizing cycles in a torus T8. The Cayley calibration form can be used to find all volume minimizing cycles in each homology class of T8. In order to apply the Cayley form to 8-dimensional tori, we need to understand the finite symmetry of the Cayley form, which has a continuous symmetry group Spin(7). We have found one finite symmetry group of order eight generated by three elements. We have also studied the symmetry groups of tori based on the results of H.S.M. Coxeter, and have had a simple description of the four crystallographic groups in O(8). They can be used to classify all finite symmetry groups of the Cayley form.
Recommended Citation
Song, Yinan, "Finite Invariance of Cayley Calibration Form" (2000). HMC Senior Theses. 125.
https://scholarship.claremont.edu/hmc_theses/125
