PreprintCC BY 4.0arXiv
Orthogonal group sections via light bulb systems
Abstract
For any oriented, smooth $4$--manifold X diffeomorphic to (S2× S2)# n# D4, this paper shows that the natural group homomorphism Mod(X,∂ X)→ O(H2(X;ℤ)) admits a section. In fact, every light bulb system in X gives rise to a section, which can be characterized uniquely in terms of implanted barbell twists and implanted crossbell involutions. Moreover, all sections arising from different light bulb systems become identical after a single S2× S2--stabilization of X.
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BibTeX
@misc{liu2026orthogonal,
title = {{Orthogonal group sections via light bulb systems}},
author = {Yi Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27126},
eprint = {2610.27126},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27126},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Orthogonal group sections via light bulb systems
AU - Yi Liu
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27126
UR - https://arxiv.org/abs/2610.27126
AB - For any oriented, smooth $4$--manifold X diffeomorphic to (S^2× S^2)^# n# D^4, this paper shows that the natural group homomorphism Mod(X,∂ X)→ O(H_2(X;ℤ)) admits a section. In fact, every light bulb system in X gives rise to a section, which can be characterized uniquely in terms of implanted barbell twists and implanted crossbell involutions. Moreover, all sections arising from different light bulb systems become identical after a single S^2× S^2--stabilization of X.
ER -