The unfiltered Hochschild–orbifold cohomology conjecture for projective symplectic quotient orbifolds

Let X\mathscr{X} be a projective symplectic quotient orbifold, and write H ⁣H(X)H\! H^\bullet(\mathscr{X}) for its Hochschild cohomology and Horb(X)H^\bullet_\mathrm{orb}(\mathscr{X}) for its orbifold cohomology. Unfiltered Hochschild–orbifold cohomology conjecture. There is an algebra isomorphism

H ⁣H(X)Horb(X).H\! H^\bullet(\mathscr{X})\cong H^\bullet_\mathrm{orb}(\mathscr{X}).

This is stronger than the associated-graded comparison and is stated as strongly related to a conjecture of Ruan. The supplied source gives no resolution.

Sources & referencesView supporting material

Primary source

Cris Negron, Travis Schedler, Pieter Belmans and Pavel Etingof, “The Hochschild cohomology ring of a global quotient orbifold”, arXiv:1809.08715 (2018).

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