{"id":57536,"date":"2024-08-07T10:59:16","date_gmt":"2024-08-07T09:59:16","guid":{"rendered":"https:\/\/www.istegroup.com\/?post_type=product&p=57536"},"modified":"2024-08-07T11:13:39","modified_gmt":"2024-08-07T10:13:39","slug":"poincare-lemma-on-differential-forms-and-connections-with-cech-de-rham-dolbeault-cohomologies","status":"publish","type":"product","link":"https:\/\/www.istegroup.com\/fr\/produit\/poincare-lemma-on-differential-forms-and-connections-with-cech-de-rham-dolbeault-cohomologies\/","title":{"rendered":"Poincar\u00e9 Lemma on Differential Forms and Connections with \u010cech-De Rham-Dolbeault Cohomologies"},"content":{"rendered":"

Poincar\u00e9 Lemma on Differential Forms and Connections with \u010cech-De Rham-Dolbeault Cohomologies<\/em> deals with the connections between \u010cech-De Rham-Dolbeault cohomologies and the Dolbeault- Grothendieck lemma. It begins by discussing one-parameter groups of diffeomorphisms or flow, Lie derivative and interior products, as well as Cartan\u2019s formula and the Poincar\u00e9 lemma on differential forms.<\/p>\n

Throughout the book, we study sheaves, \u010cech cohomology and De Rham cohomology, and present some of their most basic properties. We also explore the Mayer-Vietoris sequence by demonstrating its use when calculating the cohomology group of the sphere. We introduce the K\u00fcnneth formula (and as an application) and compute the cohomology of the torus.<\/p>\n

The final sections of the book study the delta bar-Poincar\u00e9 lemma \u2013 as well as the Dolbeault-Grothendieck lemma and its consequences \u2013 while also proving the delta bar-Poincar\u00e9 lemma in one variable, the Grothendieck Poincar\u00e9 lemma, and the Dolbeault\u2019s theorem when establishing the isomorphism between Dolbeault and \u010cech cohomology. Some results related to the connections, curvature and first Chern class of line bundles are also given. The text is enriched by concrete examples, along with exercises and their solutions.<\/p>","protected":false},"excerpt":{"rendered":"

Cet ouvrage est uniquement disponible en version \u00e9lectronique.<\/strong><\/p>\n

\n","protected":false},"featured_media":57541,"template":"","meta":{"_acf_changed":false,"_links_to":"","_links_to_target":""},"product_brand":[],"product_cat":[3262],"product_tag":[],"class_list":{"0":"post-57536","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-non-classe","8":"first","9":"instock","10":"shipping-taxable","11":"purchasable","12":"product-type-variable"},"acf":[],"yoast_head":"\nPoincar\u00e9 Lemma on Differential Forms and Connections with \u010cech-De Rham-Dolbeault Cohomologies - ISTE Group<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.istegroup.com\/produit\/poincare-lemma-on-differential-forms-and-connections-with-cech-de-rham-dolbeault-cohomologies\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Poincar\u00e9 Lemma on Differential Forms and Connections with \u010cech-De Rham-Dolbeault Cohomologies - ISTE Group\" \/>\n<meta property=\"og:description\" content=\"[:fr]Cet ouvrage est uniquement disponible en version \u00e9lectronique. 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