Realising automorphisms of the extended intersection form by diffeomorphisms
Abstract
Suppose that f : M → B is a normal (q−1)-smoothing of a 2q-manifold M over some (B,ξ), where q is even and B is simply-connected. A diffeomorphism of M over B induces an automorphism of the extended intersection form (or ``Q-form") of f, which consists of the intersection form of M and the induced homomorphism Hq(f). Assuming that Hq(B) is free, we determine precisely which automorphisms can be realised by such diffeomorphisms. In particular, if Hq−1(B) is also free, then we show that every automorphism can be realised. These results are obtained by studying a ``two-sided" version of the extended surgery obstruction, which was introduced in earlier work of the author. As an application, we show that for a complex q-dimensional complete intersection, with q > 2 even, every automorphism of the cohomology ring is realised by a diffeomorphism.
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BibTeX
@misc{nagy2026realising,
title = {{Realising automorphisms of the extended intersection form by diffeomorphisms}},
author = {Csaba Nagy},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.24617},
eprint = {2608.24617},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24617},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Realising automorphisms of the extended intersection form by diffeomorphisms
AU - Csaba Nagy
PY - 2026
DA - 2026/08/25
PB - arXiv
DO - 10.48550/arxiv.2608.24617
UR - https://arxiv.org/abs/2608.24617
AB - Suppose that f : M → B is a normal (q−1)-smoothing of a 2q-manifold M over some (B,ξ), where q is even and B is simply-connected. A diffeomorphism of M over B induces an automorphism of the extended intersection form (or ``Q-form") of f, which consists of the intersection form of M and the induced homomorphism H_q(f). Assuming that H_q(B) is free, we determine precisely which automorphisms can be realised by such diffeomorphisms. In particular, if H_q−1(B) is also free, then we show that every automorphism can be realised. These results are obtained by studying a ``two-sided" version of the extended surgery obstruction, which was introduced in earlier work of the author. As an application, we show that for a complex q-dimensional complete intersection, with q > 2 even, every automorphism of the cohomology ring is realised by a diffeomorphism.
ER -