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- W3099819028 abstract "We study a cohomology theory $$H^{bullet }_{varphi }$$ , which we call the $${mathcal {L}}_B$$ -cohomology, on compact torsion-free $$mathrm {G}_2$$ manifolds. We show that $$H^k_{varphi } cong H^k_{mathrm {dR}}$$ for $$k ne 3, 4$$ , but that $$H^k_{varphi }$$ is infinite-dimensional for $$k = 3,4$$ . Nevertheless, there is a canonical injection $$H^k_{mathrm {dR}} rightarrow H^k_{varphi }$$ . The $${mathcal {L}}_B$$ -cohomology also satisfies a Poincaré duality induced by the Hodge star. The establishment of these results requires a delicate analysis of the interplay between the exterior derivative $$mathrm {d}$$ and the derivation $${mathcal {L}}_B$$ and uses both Hodge theory and the special properties of $$mathrm {G}_2$$ -structures in an essential way. As an application of our results, we prove that compact torsion-free $$mathrm {G}_2$$ manifolds are ‘almost formal’ in the sense that most of the Massey triple products necessarily must vanish." @default.
- W3099819028 created "2020-11-23" @default.
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- W3099819028 date "2018-09-25" @default.
- W3099819028 modified "2023-09-26" @default.
- W3099819028 title "The $${mathcal {L}}_B$$ L B -cohomology on compact torsion-free $$mathrm {G}_2$$ G 2 manifolds and an application to ‘almost’ formality" @default.
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- W3099819028 doi "https://doi.org/10.1007/s10455-018-9629-x" @default.
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