PreprintarXiv licencearXiv
The homology cobordism group is not generated by graph homology $3$-spheres
Abstract
We show the homology cobordism group of homology $3$-spheres is not generated by graph homology $3$-spheres. Our technique is a combination of filtered instanton Floer theory and Gromov's simplicial volume.
Related
- The group generated by a graph's derangements
- Graph Representation via Elements of Discrete Morse and Cobordism Theories
- Fox-Milnor condition for concordant knots in homology 3-spheres
- Splice formulae for Poincaré series of integral homology spheres
- Sasaki-Einstein rational homology spheres, rational varieties and the Berglund-Hübsch rule
BibTeX
@misc{mares2026homology,
title = {{The homology cobordism group is not generated by graph homology $3$-spheres}},
author = {Ben Mares and Yuta Nozaki and Masaki Taniguchi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15415},
eprint = {2609.15415},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15415},
}
RIS
TY - UNPB
TI - The homology cobordism group is not generated by graph homology $3$-spheres
AU - Ben Mares
AU - Yuta Nozaki
AU - Masaki Taniguchi
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15415
UR - https://arxiv.org/abs/2609.15415
AB - We show the homology cobordism group of homology $3$-spheres is not generated by graph homology $3$-spheres. Our technique is a combination of filtered instanton Floer theory and Gromov's simplicial volume.
ER -