Results 11 to 20 of about 197,645 (46)

Topologization of electron liquids with Chern-Simons theory and quantum computation [PDF]

arXiv, 2006
We discuss a nexus among quantum topology, quantum physics and quantum computing.
arxiv  

A note on topological invariants in condensed matter [PDF]

arXiv, 2014
We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time reversal invariant or if there are more phases that has different topological invariants. From a mathematical point
arxiv  

Butterflies and topological quantum numbers [PDF]

arXiv, 2001
The Hofstadter model illustrates the notion of topological quantum numbers and how they account for the quantization of the Hall conductance. It gives rise to colorful fractal diagrams of butterflies where the colors represent the topological quantum numbers.
arxiv  

Topological quantum numbers in the Hall effect [PDF]

arXiv, 2003
Topological quantum numbers account for the precise quantization that occurs in the integer Hall effect. In this theory, Kubo's formula for the conductance acquires a topological interpretation in terms of Chern numbers and their non-commutative analog, the Fredholm Indices.
arxiv  

Comment on the paper "Does Zeeman's Fine Topology Exist?" at arXiv:1003.3703v1 [PDF]

arXiv, 2011
A constructive and straightforward proof of the existence of the Zeeman topology is provided, contradicting a fallacious claim contained in the paper "Does Zeeman's Fine Topology Exist?" available at arXiv:1003.3703v1.
arxiv  

Index theory and noncommutative geometry of topological insulator [PDF]

arXiv, 2018
In this chapter, we report the recent progress in the understanding of the rich mathematical structures of topological insulators in the framework of index theory and noncommutative geometry.
arxiv  

Topological Homotopy Groups [PDF]

Bulletin of the Belgian Mathematical Society, 15:3 (2008) 588-600, 2011
D. K. Biss (Topology and its Applications 124 (2002) 355-371) introduced the topological fundamental group and presented some interesting basic properties of the notion. In this article we intend to extend the above notion to homotopy groups and try to prove some similar basic properties of the topological homotopy groups.
arxiv  

By Their Fruits Ye Shall Know Them: Some Remarks on the Interaction of General Topology with Other Areas of Mathematics [PDF]

, 1999
Teun Koetsier, Jan van Mill
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Computational and applied topology, tutorial [PDF]

arXiv, 2018
This is a tutorial in applied and computational topology and topological data analysis. It is illustrated with numerous computational examples that utilize Gudhi library. It is under constant development, so please do not consider this version as final.
arxiv  

Topology and life: In search of general mathematical principles in biology and sociology [PDF]

, 1955
N. Rashevsky
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