Involutive Floer Invariants for Closed Four-Manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911608161173504 |
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| author | Brass, Owen |
| author_facet | Brass, Owen |
| contents | Inspired by the Ozsváth-Szabó mixed invariant in ordinary Heegaard Floer theory, we define a mixed invariant $Φ_{X, \mathfrak{s}}^{I}$ for closed, spin four-manifolds $(X, \mathfrak{s})$ using the cobordism maps on involutive Heegaard Floer homology. The invariant is well-defined whenever $b_{2}^{+}(X) > 4$. We furthermore construct an involutive Seiberg-Witten invariant that is well-defined whenever $b_{2}^{+}(X) > 3$. We show that these involutive invariants obstruct the existence of disjoint pairs of embedded surfaces which both violate the adjunction inequality. As an application, we find that $K3\#(S^2 \times S^2)$ contains no such pair. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18275 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Involutive Floer Invariants for Closed Four-Manifolds Brass, Owen Geometric Topology 57R58 (Primary) 57K41, 57R40 (Secondary) Inspired by the Ozsváth-Szabó mixed invariant in ordinary Heegaard Floer theory, we define a mixed invariant $Φ_{X, \mathfrak{s}}^{I}$ for closed, spin four-manifolds $(X, \mathfrak{s})$ using the cobordism maps on involutive Heegaard Floer homology. The invariant is well-defined whenever $b_{2}^{+}(X) > 4$. We furthermore construct an involutive Seiberg-Witten invariant that is well-defined whenever $b_{2}^{+}(X) > 3$. We show that these involutive invariants obstruct the existence of disjoint pairs of embedded surfaces which both violate the adjunction inequality. As an application, we find that $K3\#(S^2 \times S^2)$ contains no such pair. |
| title | Involutive Floer Invariants for Closed Four-Manifolds |
| topic | Geometric Topology 57R58 (Primary) 57K41, 57R40 (Secondary) |
| url | https://arxiv.org/abs/2604.18275 |