Novel Encodings of Homology, Cohomology, and Characteristic Classes

Itai Maimon

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arXiv · 2511.03920

Novel Encodings of Homology, Cohomology, and Characteristic Classes

Itai Maimon

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Abstract

Topological quantum error-correcting codes (QECC) encode a variety of topological invariants in their code space. A classic structure that has not been encoded directly is that of obstruction classes of a fiber bundle, such as the Chern or Euler class. Here, we construct and analyze extensions of toric codes. We then analyze the topological structure of their errors and finally construct a novel code using these errors to encode the obstruction class to a fiber bundle. In so doing, we construct an encoding of characteristic classes such as the Chern and Pontryagin class in topological QECC. An example of the Euler class of $S^2$ is constructed explicitly.

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Itai Maimon. 2025-11-05. Novel Encodings of Homology, Cohomology, and Characteristic Classes. https://arxiv.org/abs/2511.03920

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