Triangular bases of unimodular bilinear lattices and induced structures automorphism groups, vanishing cycles, monodromy groups, braid group actions and moduli spaces Claus Hertling, Khadija Larabi

Format:

Book

Author/Creator:

Hertling, Claus, author.

Larabi, Khadija, 1994- author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 2398.

Lecture notes in mathematics 1617-9692 volume 2398

Language:

English

Subjects (All):

Lattice theory.

Bilinear forms.

Physical Description:

1 online resource

Place of Publication:

Cham, Switzerland Springer [2026]

Summary:

"This monograph presents a structured and conceptually unified study of upper triangular integer matrices and the rich family of structures they induce. Central objects 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. To a given matrix is associated a ℤ-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. General 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. The book is intended for researchers and students working with integral upper triangular matrices and their induced structures"-- Springer Nature Link

Contents:

Bilinear lattices and induced structures

Braid group actions

Braid group action on upper triangular 3 x 3 matrices

Automorphism groups

Monodromy groups and vanishing cycles

Distinguished bases in the rank 2 and rank 3 cases

Manifolds induced by the orbit of distinguished bases and the orbit of distinguished matrices

The manifolds in the rank 3 cases

Isolated hypersurface singularities

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Springer Nature Link, viewed September 25, 2026)

Other Format:

Print version Hertling, Claus Triangular bases of unimodular bilinear lattices and induced structures

ISBN:

9783032259974

3032259975

OCLC:

1617485648

Access Restriction:

Restricted for use by site license