--- _id: '10033' abstract: - lang: eng text: The ⊗*-monoidal structure on the category of sheaves on the Ran space is not pro-nilpotent in the sense of [3]. However, under some connectivity assumptions, we prove that Koszul duality induces an equivalence of categories and that this equivalence behaves nicely with respect to Verdier duality on the Ran space and integrating along the Ran space, i.e. taking factorization homology. Based on ideas sketched in [4], we show that these results also offer a simpler alternative to one of the two main steps in the proof of the Atiyah-Bott formula given in [7] and [5]. acknowledgement: 'The author would like to express his gratitude to D. Gaitsgory, without whose tireless guidance and encouragement in pursuing this problem, this work would not have been possible. The author is grateful to his advisor B.C. Ngô for many years of patient guidance and support. This paper is revised while the author is a postdoc in Hausel group at IST Austria. We thank him and the group for providing a wonderful research environment. The author also gratefully acknowledges the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization Homology,” Austrian Science Fund (FWF): M 2751.' article_number: '107992' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Quoc P full_name: Ho, Quoc P id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87 last_name: Ho orcid: 0000-0001-6889-1418 citation: ama: Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 2021;392. doi:10.1016/j.aim.2021.107992 apa: Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107992 chicago: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107992. ieee: Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,” Advances in Mathematics, vol. 392. Elsevier, 2021. ista: Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 392, 107992. mla: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” Advances in Mathematics, vol. 392, 107992, Elsevier, 2021, doi:10.1016/j.aim.2021.107992. short: Q.P. Ho, Advances in Mathematics 392 (2021). date_created: 2021-09-21T15:58:59Z date_published: 2021-09-21T00:00:00Z date_updated: 2023-08-14T06:54:35Z day: '21' ddc: - '514' department: - _id: TaHa doi: 10.1016/j.aim.2021.107992 external_id: arxiv: - '1610.00212' isi: - '000707040300031' file: - access_level: open_access checksum: f3c0086d41af11db31c00014efb38072 content_type: application/pdf creator: qho date_created: 2021-09-21T15:58:52Z date_updated: 2021-09-21T15:58:52Z file_id: '10034' file_name: 1-s2.0-S000187082100431X-main.pdf file_size: 840635 relation: main_file file_date_updated: 2021-09-21T15:58:52Z has_accepted_license: '1' intvolume: ' 392' isi: 1 keyword: - Chiral algebras - Chiral homology - Factorization algebras - Koszul duality - Ran space language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 26B96266-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02751 name: Algebro-Geometric Applications of Factorization Homology publication: Advances in Mathematics publication_identifier: eissn: - 1090-2082 issn: - 0001-8708 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: The Atiyah-Bott formula and connectivity in chiral Koszul duality tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 392 year: '2021' ...