Topological Classification of Endomorphisms of Complex Line Bundles

1979 ◽  
Vol s2-20 (1) ◽  
pp. 152-160
Author(s):  
D. W. Bass
Keyword(s):  
Topological Classification ◽  
Line Bundles ◽  
Complex Line ◽  
Complex Line Bundles

scholarly journals On a construction in bordism theory

1986 ◽  
Vol 29 (3) ◽  
pp. 413-422 ◽  
Author(s):  
Nigel Ray
Keyword(s):  
Line Bundles ◽  
Complex Line ◽  
Surgery Theory ◽  
Normal Bundles ◽  
Bordism Ring ◽  
Complex Line Bundles

In [2], R. Arthan and S. Bullett pose the problem of representing generators of the complex bordism ring MU* by manifolds which are totally normally split; i.e. whose stable normal bundles are split into a sum of complex line bundles. This has recently been solved by Ochanine and Schwartz [8] who use a mixture of J-theory and surgery theory to establish several results, including the following.

ASYMPTOTIC BEHAVIOR OF THE GINZBURG-LANDAU FUNCTIONAL ON COMPLEX LINE BUNDLES OVER COMPACT RIEMANN SURFACES

1996 ◽  
Vol 08 (03) ◽  
pp. 457-486
Author(s):  
GIANDOMENICO ORLANDI
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Chern Class ◽  
Riemann Surfaces ◽  
Line Bundles ◽  
Complex Line ◽  
Ginzburg Landau ◽  
Renormalized Energy ◽  
Compact Riemann Surfaces ◽  
Complex Line Bundles

Motivated by the works of F. Bethuel, H. Brezis, F. Hélein [5] and of F. Bethuel, T. Rivière [6], an asymptotic analysis is carried out for minimizers of the Ginzburg-Landau functional depending on a parameter ε, in the more general case of complex line bundles with prescribed Chern class over compact Riemann surfaces. Such a functional describes a 2-dimensional abelian Higgs model and is also related to phenomena in superconductivity. A suitable renormalized energy is defined which characterizes the singularities (degree one vortices) of the limiting configuration.

COMPLEX LINE BUNDLES OVER TWO-SPHERE AND BLACK HOLE PHYSICS

1994 ◽  
Vol 09 (34) ◽  
pp. 3175-3183 ◽  
Author(s):  
YU. P. GONCHAROV ◽  
J.V. YAREVSKAYA
Keyword(s):  
Black Hole ◽  
Black Hole Physics ◽  
Dimensional Space ◽  
Line Bundles ◽  
Complex Line ◽  
Schwarzschild Black Hole ◽  
Complex Scalar ◽  
Complex Scalar Field ◽  
Standing Problem ◽  
Complex Line Bundles

We discuss a long-standing problem of the global topological non-trivial properties of the four-dimensional space-times underlying black hole physics and observe that the standard space-time topology of the ℝ2×S2 form for black hole physics admits topologically inequivalent configurations of a complex scalar field on black hole by virtue of the availability of non-trivial complex line bundles over S2. Each configuration can be labeled by its Chern number n∈ℤ. For the Schwarzschild black hole we formulate an appropriate wave equation for these configurations in massless case and describe its solutions as a first step to study quantum effects for the above configurations within the framework of black hole physics.

MONOPOLES OVER FUZZY TWO-SPHERE BY ONE SEQUENCE OF THE IRREPS OF SU(2)

2011 ◽  
Vol 26 (39) ◽  
pp. 2973-2981 ◽  
Author(s):  
A. DEHGHANI ◽  
H. FAKHRI ◽  
A. HASHEMI ◽  
M. LOTFIZADEH ◽  
B. MOJAVERI
Keyword(s):  
Tensor Product ◽  
Finite Sequence ◽  
Line Bundles ◽  
Projective Modules ◽  
Complex Line ◽  
Fuzzy Sphere ◽  
Chern Numbers ◽  
Topological Charges ◽  
Complex Line Bundles

The purpose of this paper is to use the idea in J. Geom. Phys.42, 54 (2002) to compute the topological charges for a (finite) sequence of noncommutative line bundles over the fuzzy sphere. Central to this task is to construct projective modules associated with sequence of the irreducible sub-representations of the tensor product of two different irreps of SU (2). The topological charges corresponding to such fuzzy line bundles are fractional and different from each other. However, in the commutative limit, those tend to Chern numbers of a sequence of the complex line bundles over two-sphere.

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