Exotic ℝ⁴'s as unions of two thickened circles

@misc{eli2026exotic,
  title = {{Exotic $\mathbbR^4$'s as unions of two thickened circles}},
  author = {Sean Eli},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19263},
  eprint = {2610.19263},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19263},
}

TY  - UNPB
TI  - Exotic ℝ^4's as unions of two thickened circles
AU  - Sean Eli
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.19263
UR  - https://arxiv.org/abs/2610.19263
AB  - We give an infinite family of non-diffeomorphic exotic ℝ^4's, each of which is the union of two copies of a standard open tubular neighborhood of the circle, which intersect in a standard open tubular neighborhood of the wedge of two circles. This gives the simplest known decomposition of an exotic ℝ^4 into two open sets, making progress on Question 4.43 (A) of Kirby's 1995 problem list. The decompositions are obtained by studying fibered slice disk complements in certain Casson-Gordon homotopy 4-balls, for which we provide similar decompositions. We distinguish the ℝ^4's using end Floer homology.
ER  -