{"paper":{"title":"Intersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant Mahowald Invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.AT","authors_text":"Jianfeng Lin, Michael J. Hopkins, XiaoLin Danny Shi, Zhouli Xu","submitted_at":"2018-12-10T19:39:51Z","abstract_excerpt":"In studying the \"11/8-Conjecture\" on the Geography Problem in 4-dimensional topology, Furuta proposed a question on the existence of Pin(2)-equivariant stable maps between certain representation spheres. In this paper, we present a complete solution to this problem by analyzing the Pin(2)-equivariant Mahowald invariants. As a geometric application of our result, we prove a \"10/8+4\"-Theorem.\n  We prove our theorem by analyzing maps between certain finite spectra arising from BPin(2) and various Thom spectra associated with it. To analyze these maps, we use the technique of cell diagrams, known "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04052","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}