PreprintarXiv licencearXiv
Logarithmic transformations on the six-sphere
Abstract
We show that there are infinitely many choices of the multiplicities in the logarithmic transformation step of the Alpöge--Claude construction which produce a complex threefold diffeomorphic to the six-sphere. Moreover, distinct choices of the multiplicities yield biholomorphically inequivalent complex structures.
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BibTeX
@misc{viaclovsky2026logarithmic,
title = {{Logarithmic transformations on the six-sphere}},
author = {Jeff Viaclovsky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39102},
eprint = {2610.39102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39102},
}
RIS
TY - UNPB
TI - Logarithmic transformations on the six-sphere
AU - Jeff Viaclovsky
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39102
UR - https://arxiv.org/abs/2610.39102
AB - We show that there are infinitely many choices of the multiplicities in the logarithmic transformation step of the Alpöge--Claude construction which produce a complex threefold diffeomorphic to the six-sphere. Moreover, distinct choices of the multiplicities yield biholomorphically inequivalent complex structures.
ER -