منابع مشابه
The Hopf Fibration over S Admits No S-subfibration*
It is shown that there does not exist a PL-bundle over S8 with fibre and total space PL-manifolds homotopy equivalent to CP and CP respectively. Consequently, the Hopf fibration over S8 admits no subfibration by PL-circles.
متن کاملThe Hopf Fibration and its Applications
Among the most important topological constructions are Hopf fibrations. That they both play an important role in topology itself and have numerous physical applications lends credence to this statement. In this paper, I will discuss some of these applications as motivation for mathematicians to learn about the physical significance of the Hopf fibration in greater detail than that presented her...
متن کاملAnalysis of the Horizontal Laplacian for the Hopf Fibration
We study the horizontal Laplacian ∆ associated to the Hopf fibration S → S with arbitrary Chern number k. We use representation theory to calculate the spectrum, describe the heat kernel and obtain the complete heat trace asymptotics of ∆ . We express the Green functions for associated Poisson semigroups and obtain bounds for their contraction properties and Sobolev inequalities for ∆ . The bou...
متن کاملThe Cayley-Dickson Construction in Homotopy Type Theory
We define in the setting of homotopy type theory an H-space structure on S3. Hence we obtain a description of the quaternionic Hopf fibration S3 ↪→ S7 S4, using only homotopy invariant tools.
متن کاملGenerating the Hopf fibration experimentally in nematic liquid crystals.
The Hopf fibration is an example of a texture: a topologically stable, smooth, global configuration of a field. Here we demonstrate the controlled sculpting of the Hopf fibration in nematic liquid crystals through the control of point defects. We demonstrate how these are related to torons by use of a topological visualization technique derived from the Pontryagin-Thom construction.
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1975
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000016780