EXPOSITIO

A home for expository scholarship

Expositio is a repository for expository papers in a wide range of academic disciplines, supporting preprints, revisions, optional peer review, saved papers, and overlay journals.

3 Papers in view

What is Expositio?

A public repository for expository academic papers, with an integrated scholarly record.

Expositio is a place to read and cite expository work. Papers are published as stable, citable records, while remaining connected to later versions, editorial decisions, and related context.

Some papers are early drafts; others have been peer reviewed or formally published. Each paper remains readable on its own, while preserving the history behind it.

The result is both a reading room and a record: a place to browse by field, read papers in stable form, and follow their development over time.

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Differential geometry

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Mathematics Differential geometry
Domain: Mathematics × Branch: Differential geometry ×

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v1

The Fundamental Theorem of Calculus, Green's theorem, the classical Stokes theorem, and the divergence theorem each relate differentiation on a region to integration on its boundary. This paper develops the language of smooth manifolds and differential forms in which these r…

Mathematics / Global analysis, analysis on manifolds Mathematics / Algebraic geometry Mathematics / Differential geometry Mathematics / Linear and multilinear algebra; matrix theory
Mathematics > Global analysis, analysis on manifolds > de Rham theory in global analysis Primary
Mathematics > Algebraic geometry > de Rham cohomology and algebraic geometry
Mathematics > Differential geometry > Integral geometry; differential forms, currents, etc.
Mathematics > Linear and multilinear algebra; matrix theory > Exterior algebra, Grassmann algebras
v1

Hyperbolic geometry is a non-Euclidean geometry where geodesics play the role of straight lines. It is characterised by a constant negative curvature. The idea was conceived when mathematicians tried to understand the parallel postulate. This expository paper develops the founda…

Mathematics / Differential geometry Mathematics / Geometry Mathematics / Topological groups, Lie groups Mathematics / Functions of a complex variable
Mathematics > Differential geometry > Research exposition (monographs, survey articles) pertaining to differential geometry Primary
Mathematics > Geometry > Classical or axiomatic geometry and physics
Mathematics > Topological groups, Lie groups > Structure and representation of the Lorentz group
Mathematics > Functions of a complex variable > General theory of conformal mappings

Expositio paper

Group Actions and Möbius Symmetries in Hyperbolic Tessellations

AJ, Aaditya Bilakanti, Palaash Gang

Preprint
v1

This expository paper explains tessellations of the hyperbolic plane from a differential-geometric viewpoint. We review the upper half-plane (H) and Poincaré disk (D) models and the Cayley transform linking them. We prove that orientation-preserving isometries are precisely PSL(…

Mathematics / Differential geometry
Mathematics > Differential geometry > Methods of global Riemannian geometry, including PDE methods; curvature restrictions Primary
Mathematics > Differential geometry > Differential geometry of symmetric spaces
Mathematics > Differential geometry > Geodesics in global differential geometry