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Topology"],"published-print":{"date-parts":[[2025,12]]},"abstract":"Abstract<\/jats:title>\n \n We present small triangulations of all connected sums of\n \n \n $$\\mathbb{C}\\mathbb{P}^2$$<\/jats:tex-math>\n \n \n C<\/mml:mi>\n \n \n P<\/mml:mi>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and\n \n \n $$S^2 \\times S^2$$<\/jats:tex-math>\n \n \n \n S<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n \u00d7<\/mml:mo>\n \n S<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n with the standard piecewise linear structure. Our triangulations have\n \n \n $$2\\beta _2+2$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \n \u03b2<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n +<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n pentachora, where\n \n \n $$\\beta _2$$<\/jats:tex-math>\n \n \n \u03b2<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is the second Betti number of the manifold. By a conjecture of the authors and, independently, Burke, these triangulations have the smallest possible number of pentachora for their respective topological types.\n <\/jats:p>","DOI":"10.1007\/s41468-025-00221-z","type":"journal-article","created":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T09:54:32Z","timestamp":1760003672000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Small triangulations of simply connected 4-manifolds"],"prefix":"10.1007","volume":"9","author":[{"given":"Jonathan","family":"Spreer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucy","family":"Tobin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,9]]},"reference":[{"key":"221_CR1","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/BF03026567","volume":"5","author":"TF Banchoff","year":"1983","unstructured":"Banchoff, T.F., K\u00fchnel, W.: The 9-vertex complex projective plane. 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