Skip to content
DraconiticResearch
Search Sources API
197,688 studies31 sourcesUpdated 9 min ago
PreprintarXiv licencearXiv

The Coarse Novikov Conjecture for Finite Products of Fibred Coarsely Embeddable Spaces

  • Liang Guo
  • Zheng Luo
  • Qin Wang
Open at sourcePDFDOICite

Abstract

In this paper, we prove that the coarse Novikov conjecture holds for finite products of bounded-geometry proper metric spaces whose factors admit fibred coarse embeddings into possibly different target spaces. A key ingredient is the construction of suitable coarsely proper algebras adapted to product spaces. Our other main tool is an iterated approach to relative higher index theory. By constructing the corresponding multi-stage Roe algebras and index maps, we establish a reduction theorem that bridges these iterated relative statements with the global coarse Novikov conjecture.

Related

  1. Higher-order jet and its application to the Novikov conjecture
    Jintao Deng, Geng Tian
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Embedding complexity into the universal Banach space and the strong Novikov conjecture
    Geng Tian, Guoliang Yu
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Pólya’s conjecture for thin products
    Xiang He, Zuoqin Wang
    International Mathematics Research NoticesPeer-reviewedLicence not statedFull text12 citedMathematical physicsOpenAlex
  4. Combination Theorems and the Farrell--Jones Conjecture for Graph Products of Pairs
    I. Gkeneralis, S. Prassidis
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  5. The Dynamical Mordell--Lang Conjecture for Relatively Étale Systems over Products of Curves
    Bhawesh Mishra
    arXivPreprintCC BY-NC-SA 4.0Full textAlgebra & number theoryDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{guo2026coarse,
  title = {{The Coarse Novikov Conjecture for Finite Products of Fibred Coarsely Embeddable Spaces}},
  author = {Liang Guo and Zheng Luo and Qin Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26643},
  eprint = {2609.26643},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26643},
}
RIS
TY  - UNPB
TI  - The Coarse Novikov Conjecture for Finite Products of Fibred Coarsely Embeddable Spaces
AU  - Liang Guo
AU  - Zheng Luo
AU  - Qin Wang
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26643
UR  - https://arxiv.org/abs/2609.26643
AB  - In this paper, we prove that the coarse Novikov conjecture holds for finite products of bounded-geometry proper metric spaces whose factors admit fibred coarse embeddings into possibly different target spaces. A key ingredient is the construction of suitable coarsely proper algebras adapted to product spaces. Our other main tool is an iterated approach to relative higher index theory. By constructing the corresponding multi-stage Roe algebras and index maps, we establish a reduction theorem that bridges these iterated relative statements with the global coarse Novikov conjecture.
ER  -