Rationally slice knots that are not biprojectively H-slice

@misc{brod2026rationally,
  title = {{Rationally slice knots that are not biprojectively H-slice}},
  author = {Elise Brod},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41996},
  eprint = {2610.41996},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41996},
}

TY  - UNPB
TI  - Rationally slice knots that are not biprojectively H-slice
AU  - Elise Brod
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41996
UR  - https://arxiv.org/abs/2610.41996
AB  - We show that rationally slice knots need not be biprojectively H-slice (BPH-slice), answering a question in the study of the rational knot concordance group. Our main tool is a lattice embedding obstruction to H-sliceness in #^nℂℙ^2 for knots with vanishing signature, extending work of Kjuchukova--Miller--Ray--Sakallı. We apply the obstruction to an infinite family of rationally slice knots, beginning with 8_18. As additional applications, we obstruct the BPH-sliceness of a family of 2-bridge knots which is not obstructed by the instanton knot concordance invariant r_0, we obstruct a non-alternating family of Montesinos knots, and we give prime alternating knots that are topologically but not smoothly biprojectively H-slice. We discuss why these knots remain plausible candidates for detecting exotic smooth structures on #^nℂℙ^2 and suggest natural sources of further candidates.
ER  -