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Defect TQFTs, the Generalized Cobordism Hypothesis, and Algebraic K-Theory

  • Keyao Peng
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Abstract

By constructing a fully dualizable category Bord๐’žn as the left adjoint of the forgetful functor, we state a generalized cobordism hypothesis. As a corollary, we establish a generalized Pontryagin-Thom isomorphism that gives a geometric interpretation of higher algebraic K-theory using cobordism classes of framed manifolds and stratified spaces decorated by categorical string diagrams, which we call lasagnas. For finite-dimensional vector spaces over a field, these decorations are branched local systems. We also examine low-dimensional representatives, including K1, Steinberg-group presentations of K2, and fillings related to the Steinberg relation, providing a more explicit construction of Ghys' manifold.

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Cite

BibTeXRIS
BibTeX
@misc{peng2026defect,
  title = {{Defect TQFTs, the Generalized Cobordism Hypothesis, and Algebraic $K$-Theory}},
  author = {Keyao Peng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41105},
  eprint = {2610.41105},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41105},
}
RIS
TY  - UNPB
TI  - Defect TQFTs, the Generalized Cobordism Hypothesis, and Algebraic K-Theory
AU  - Keyao Peng
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41105
UR  - https://arxiv.org/abs/2610.41105
AB  - By constructing a fully dualizable category Bord^๐’ž_n as the left adjoint of the forgetful functor, we state a generalized cobordism hypothesis. As a corollary, we establish a generalized Pontryagin-Thom isomorphism that gives a geometric interpretation of higher algebraic K-theory using cobordism classes of framed manifolds and stratified spaces decorated by categorical string diagrams, which we call lasagnas. For finite-dimensional vector spaces over a field, these decorations are branched local systems. We also examine low-dimensional representatives, including K_1, Steinberg-group presentations of K_2, and fillings related to the Steinberg relation, providing a more explicit construction of Ghys' manifold.
ER  -