{"product_id":"9783032259967","title":"Triangular Bases of Unimodular Bilinear Lattices and Induced Structures Automorphism Groups, Vanishing Cycles, Monodromy Groups, Braid Group Actions and Moduli Spaces","description":"\u003ch3\u003eLecture Notes in Mathematics\u003c\/h3\u003e\u003ch1\u003eTriangular Bases of Unimodular Bilinear Lattices and Induced Structures\u003c\/h1\u003e\u003ch2\u003eAutomorphism Groups, Vanishing Cycles, Monodromy Groups, Braid Group Actions and Moduli Spaces\u003c\/h2\u003e\u003ch3\u003eClaus Hertling | Khadija Larabi\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Algebra \/ Abstract\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp class=\"MsoNormal\" style=\"margin-bottom: 0cm; line-height: normal;\"\u003e\u003cspan style=\"font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: ZH-CN;\"\u003eThis monograph presents a structured and conceptually unified study of upper triangular integer matrices and the rich family of structures they induce. Central \u003cspan style=\"mso-spacerun: yes;\"\u003e \u003c\/span\u003eobjects include unimodular bilinear lattices, vanishing cycles, monodromy groups, braid group actions, and associated moduli spaces. These constructions naturally provide a common framework linking algebraic geometry, representation theory, singularity theory, and the theory of irregular meromorphic connections.\u003c\/span\u003e\u003cspan style=\"font-family: Aptos, sans-serif; font-size: 10pt;\"\u003e \u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"margin-bottom: 0cm; line-height: normal;\"\u003e\u003cspan style=\"font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: ZH-CN;\"\u003eTo a given matrix is associated a \u003c\/span\u003e\u003cspan style=\"font-size: 12.0pt; font-family: 'Cambria Math',serif; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Cambria Math'; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: ZH-CN;\"\u003eℤ\u003c\/span\u003e\u003cspan style=\"font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: ZH-CN;\"\u003e-lattice with a unimodular bilinear form (the Seifert form) and a triangular basis. This leads to even and odd intersection forms, reflections and transvections, monodromy groups, and corresponding vanishing cycles. Braid group actions generate orbits of distinguished bases and matrices, which in turn give rise to complex manifolds obtained by gluing Stokes regions.\u003c\/span\u003e\u003cspan style=\"font-size: 10.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Liberation Mono'; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: ZH-CN;\"\u003e \u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"margin-bottom: 0cm; line-height: normal;\"\u003e\u003cspan style=\"font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: ZH-CN;\"\u003eGeneral tools and results are developed throughout, with a systematic analysis of the cases of rank 2 and 3. Already in rank 3 a wide range of phenomena appears, illustrating the broader landscape. Classical situations related to Coxeter groups, generalized Cartan lattices, exceptional sequences, and isolated hypersurface singularities arise as special cases but represent only a small part of the theory. \u003c\/span\u003e\u003cspan style=\"font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: Calibri; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: ZH-CN;\"\u003eThe book is intended for researchers and students working with integral upper triangular matrices and their induced structures.\u003c\/span\u003e\u003c\/p\u003e\n\u003c\/div\u003e\u003cdiv\u003e\n\u003cp class=\"MsoNormal\" style=\"margin-bottom: 0cm; line-height: normal;\"\u003e\u003cstrong\u003e\u003cspan style=\"font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: 'Times New Roman'; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: EN-GB;\"\u003eClaus Hertling\u003c\/span\u003e\u003c\/strong\u003e\u003cspan style=\"font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: 'Times New Roman'; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: EN-GB;\"\u003e is a Professor at the University of Mannheim. His research interests are in isolated hypersurface singularities and their moduli spaces, Frobenius manifolds, meromorphic connections and, more recently, integral matrices in the contexts of Stokes structures and monodromy.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp class=\"MsoNormal\" style=\"mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; line-height: normal;\"\u003e\u003cstrong\u003e\u003cspan style=\"font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: 'Times New Roman'; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: EN-GB;\"\u003eKhadija\u003cspan style=\"background: white;\"\u003e Larabi\u003c\/span\u003e\u003c\/span\u003e\u003c\/strong\u003e\u003cspan style=\"font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: 'Times New Roman'; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; color: black; background: white; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: EN-GB;\"\u003e obtained her PhD\u003c\/span\u003e\u003cspan style=\"font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: 'Times New Roman'; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: EN-GB;\"\u003e from the University of Mannheim. She works on algebraic structures induced by upper triangular integral matrices and on orders and full lattices in finite-dimensional commutative \u003c\/span\u003e\u003cspan style=\"font-size: 12.0pt; font-family: 'Cambria Math',serif; mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Cambria Math'; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: EN-GB;\"\u003eℚ\u003c\/span\u003e\u003cspan style=\"font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: 'Times New Roman'; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri; color: black; mso-font-kerning: 0pt; mso-ligatures: none; mso-fareast-language: EN-GB;\"\u003e-algebras.\u003c\/span\u003e\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e22 August 2026\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eDeutsche Forschungsgemeinschaft\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783032259967\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e403\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Deutsche Forschungsgemeinschaft","offers":[{"title":"Default Title","offer_id":47182667022476,"sku":"9783032259967","price":76.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783032259967.jpg?v=1780591529","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783032259967","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}