HOMOTOPY GROUP OF SPHERES, HOPF FIBRATIONS AND VIL-LARCEAU CIRCLES
نویسندگان
چکیده
Unlike geometry, spheres in topology have been seen as topological invariants, where their structures are defined spaces. Forgetting, the exact notion of and impossibility embedding one into other, homotopy relates how sphere i dimensions can wrap another n dimensions.
منابع مشابه
Geometry of Entangled States , Bloch Spheres and Hopf Fibrations
We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the 3-dimensional sphere S. The S base space of a suitably oriented S Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the qubit o...
متن کاملSome Cyclic Group Actions on Homotopy Spheres
In [4J Orlik defined a free cyclic group action on a homotopy sphere constructed as a Brieskorn manifold and proved the following theorem: THEOREM. Every odd-dimensional homotopy sphere that bounds a para-llelizable manifold admits a free Zp-action for each prime p. On the other hand, it was shown ([3J) that there exists a free Zp-action on a 2n-1 dimensional homotopy sphere so that its orbit s...
متن کاملCurves, Circles, and Spheres
The standard radius of curvature at a point q(s) on a smooth curve can be defined as the limiting radius of circles through three points that all coalesce to q(s). In the study of ideal knot shapes it has recently proven useful to consider a global radius of curvature of the curve at q(s) defined as the smallest possible radius amongst all circles passing through this point and any two other po...
متن کاملParametric circles and spheres
Formulations for parametric circles and spheres in terms of rational Gaussian (RaG) curves and surfaces are introduced. With the proposed formulations, a full circle is generated by interpolating a closed RaG curve to the vertices of an equilateral triangle, and a full sphere is generated by interpolating a closed RaG surface to the vertices of an octahedron with equilateral triangular faces. G...
متن کاملOn Quotients of Hopf Fibrations*
It was shown in [LV] that there are no PL-bundles of the form CPh ↪→ CPh → S where CPh denotes a PL-manifold homotopy equivalent to CP. It was stated at the end of [LV] that the homotopy analog of a) does not exist. In [U], Ucci showed that there exists no Hurewicz fibration of the form CP ↪→ CP → S. However, as stated, this was not the strongest possible result. Let HCP, HCaP and S h denote sp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: EPRA international journal of research & development
سال: 2022
ISSN: ['2455-7838']
DOI: https://doi.org/10.36713/epra11212