Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 11 min ago
PreprintarXiv licencearXiv

Exotic S^2 x S^2 candidates that are just fake

  • R. İnanç Baykur
Open at sourcePDFDOICite

Abstract

We show that two infinite families of homology S2× S2's presented in \cite{FPS, AP}, originally proposed as exotic candidates, are aspherical. In particular, none of these manifolds is an exotic S2× S2. We prove this by reconstructing them from aspherical building blocks, following Edmonds. The same arguments apply to and rule out further candidates for simply connected exotica. We also give counterexamples to the conjecture that Luttinger surgery preserves symplectic asphericity.

Related

  1. Fake quadrics with bounded cohomology property
    Sichen Li
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Explicit equations of three pairs of fake projective planes
    Lev Borisov, Nathan Mann
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Odd and even fake quadrics isogenous to a product
    Fabrizio Catanese, JongHae Keum, Do Geun Kim +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  4. Braided Multisections and Akhmedov's Fake Quadrics
    Anar Akhmedov
    arXivPreprintCC0Full textGeometry & topologyarXiv
  5. Non-split Cartan curves and a characterization of fake elliptic curves
    Enric Florit
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{baykur2026exotic,
  title = {{Exotic S^2 x S^2 candidates that are just fake}},
  author = {R. İnanç Baykur},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04634},
  eprint = {2610.04634},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04634},
}
RIS
TY  - UNPB
TI  - Exotic S^2 x S^2 candidates that are just fake
AU  - R. İnanç Baykur
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.04634
UR  - https://arxiv.org/abs/2610.04634
AB  - We show that two infinite families of homology S^2× S^2's presented in \cite{FPS, AP}, originally proposed as exotic candidates, are aspherical. In particular, none of these manifolds is an exotic S^2× S^2. We prove this by reconstructing them from aspherical building blocks, following Edmonds. The same arguments apply to and rule out further candidates for simply connected exotica. We also give counterexamples to the conjecture that Luttinger surgery preserves symplectic asphericity.
ER  -