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PreprintCC BY 4.0arXiv

Higher-order jet and its application to the Novikov conjecture

  • Jintao Deng
  • Geng Tian
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Abstract

In this paper, we apply higher-order tangent bundles and higher-order derivative maps to study countable subgroups of the deffeomorphism group Diff(M) of a closed smooth manifold M. Using this framework, we introduce the concept of higher order μ-discreteness for subgroup Γ< Diff(M). As applications, we show that both the strong Novikov conjecture and the coarse Baum--Connes conjecture hold for countable groups with higher order μ-discreteness.

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Cite

BibTeXRIS
BibTeX
@misc{deng2026higherorder,
  title = {{Higher-order jet and its application to the Novikov conjecture}},
  author = {Jintao Deng and Geng Tian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40062},
  eprint = {2610.40062},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40062},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Higher-order jet and its application to the Novikov conjecture
AU  - Jintao Deng
AU  - Geng Tian
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40062
UR  - https://arxiv.org/abs/2610.40062
AB  - In this paper, we apply higher-order tangent bundles and higher-order derivative maps to study countable subgroups of the deffeomorphism group Diff(M) of a closed smooth manifold M. Using this framework, we introduce the concept of higher order μ-discreteness for subgroup Γ< Diff(M). As applications, we show that both the strong Novikov conjecture and the coarse Baum--Connes conjecture hold for countable groups with higher order μ-discreteness.
ER  -