scholarly journals Book Review: Differential geometry of complex vector bundles

1988 ◽  
Vol 19 (2) ◽  
pp. 528-531
Author(s):  
Christian Okonek
Keyword(s):  
Differential Geometry ◽  
Vector Bundles ◽  
Complex Vector

scholarly journals Non-abelian Quantum Statistics on Graphs

2019 ◽  
Vol 371 (3) ◽  
pp. 921-973 ◽  
Author(s):  
Tomasz Maciążek ◽  
Adam Sawicki
Keyword(s):  
Quantum Computing ◽  
General Framework ◽  
Vector Bundles ◽  
Quantum Statistics ◽  
Configuration Spaces ◽  
Topological Invariants ◽  
Complex Vector ◽  
Homology Groups ◽  
Isomorphism Classes ◽  
Effective Models

Abstract We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of particles constrained to move in a topological space X. The framework involves a study of isomorphism classes of flat complex vector bundles over the configuration space of X which can be achieved by determining its homology groups. We apply this methodology for configuration spaces of graphs. As a conclusion, we provide families of graphs which are good candidates for studying simple effective models of anyon dynamics as well as models of non-abelian anyons on networks that are used in quantum computing. These conclusions are based on our solution of the so-called universal presentation problem for homology groups of graph configuration spaces for certain families of graphs.

First (fuzzy) Hopf map from irreps of SU(2)

Open Physics ◽  
2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Hossein Fakhri ◽  
Mehdi Lotfizadeh
Keyword(s):  
Vector Bundles ◽  
Hopf Fibration ◽  
Complex Vector ◽  
Spherical Basis ◽  
Hopf Map ◽  
One To One

AbstractUsing the spherical basis of the spin-ν operator, together with an appropriate normalized complex (2ν +1)-spinor on S 3 we obtain spin-ν representation of the U(1) Hopf fibration S 3 → S 2 as well as its associated fuzzy version. Also, to realize the first Hopf map via the spherical basis of the spin-1 operator with even winding numbers, we present an appropriate normalized complex three-spinor. We put the winding numbers in one-to-one correspondence with the monopole charges corresponding to different associated complex vector bundles.

Nonseparation in the moduli of complex vector bundles

1978 ◽  
Vol 235 (1) ◽  
pp. 1-16
Author(s):  
V. Alan Norton
Keyword(s):  
Vector Bundles ◽  
Complex Vector
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