A compact non‐formal closed G2 manifold with b1=1$b_1=1$. Issue 8 (16th August 2022)

• Record Type: Journal Article
• Authors: Martín‐Merchán, Lucía
• Is Part Of: Mathematische Nachrichten. Volume 295:Issue 8(2022)
• Page Start: 1562
• Page End: 1590
• Publication Date: 2022-08-16
• Subjects: closed G2 structures -- formality -- G2 orbifold resolution; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.202000452
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract: We construct a compact manifold with a closed G2 structure not admitting any torsion‐free G2 structure, which is non‐formal and has first Betti number b 1 = 1 $b_1=1$ . We develop a method of resolution for orbifolds that arise as a quotient M / Z 2 $M/{{\mathbb {Z}}_2}$ with M a closed G2 manifold under the assumption that the singular locus carries a nowhere‐vanishing closed 1‐form.