Topological Phases: Understanding Kitaev's Paper

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SUMMARY

The discussion centers on understanding Kitaev's paper "Periodic table for topological insulators and superconductors." Key challenges include the advanced mathematical concepts required, particularly from algebraic topology, such as homotopy, homology, and K-theory. The paper also emphasizes the importance of understanding Chern numbers and winding numbers for grasping the material. For those struggling with the mathematical background, the recommended resource is Nakahara's "Geometry, Topology and Physics."

PREREQUISITES
  • Algebraic topology concepts: homotopy
  • Algebraic topology concepts: homology
  • Algebraic topology concepts: K-theory
  • Understanding of Chern numbers and winding numbers
NEXT STEPS
  • Study Nakahara's "Geometry, Topology and Physics"
  • Learn about Chern numbers in the context of topological insulators
  • Explore the fundamentals of homotopy theory
  • Investigate K-theory applications in physics
USEFUL FOR

Researchers, physicists, and students in theoretical physics or mathematics who are delving into topological phases and require a solid understanding of the underlying algebraic topology concepts.

shiraz
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Dear All
I am trying to understand the following paper for Kitaev :" Periodic table for topological insulators and superconductors", But i am founding it so hard. Can anyone help me to understand it?
Thank you.
 
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Can you be more specific? There are a lot of advanced mathematical concepts to be mastered before you can hope to understand this paper, esp. from algebraic topology, such as homotopy, homology, K-theory, ...

This paper is more extensive, and constructs the table more explicitly, with direct computations of Chern numbers, winding numbers etc... However, that won't help you if you don't know what a Chern number is. If you lack the mathematical background, I recommend Nakahara: Geometry, Topology and Physics.
 

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