Key papers in Geometry and Topology
Pofolia’s corpus holds 70 papers from the Geometry and Topology subfield (2012–2026). The list below starts with the most cited.
Most cited
Ranked by citation count. Because citations accumulate over time, this list naturally leans towards work published a few years ago; for where the field is now, see “recently added”.
Introduction: Motivation
Cambridge University Press eBooks · 2020 · FWCI 163.97 · 2,278 citations
This introduction motivates a book on symplectic topology by highlighting intersection theory's role in two early theorems, one of which requires a nonobvious extension of homological intersection theory.
geomorph: an<scp>r</scp>package for the collection and analysis of geometric morphometric shape data
Methods in Ecology and Evolution · 2013 · Q1 · SJR 2.00 · FWCI 114.99 · 2,198 citations · Open access
The 'geomorph' R package is introduced, offering a comprehensive suite of tools for 2D and 3D geometric morphometric analyses, from data digitization to advanced statistical testing and visualization.
Artificial intelligence and statistics
Frontiers of Information Technology & Electronic Engineering · 2018 · Q2 · FWCI 56.15 · 1,995 citations
A new 'Population, Question of Interest, Representativeness, Scrutiny' (PQRS) workflow is proposed to integrate statistical concepts and human collaboration into AI development.
Chemical Graph Theory
2018 · FWCI 23.16 · 1,486 citations
This paper outlines the fundamental concepts and applications of chemical graph theory, a field that uses graph theory to represent and analyze molecules.
Ordinary Differential Equations and Dynamical Systems
Graduate studies in mathematics · 2012 · FWCI 32.05 · 1,175 citations
This is a preliminary version of the book "Ordinary Differential Equations and Dynamical Systems" published by the American Mathematical Society (AMS).
Size, shape, and form: concepts of allometry in geometric morphometrics
Development Genes and Evolution · 2016 · FWCI 117.31 · 1,045 citations · Open access
This review systematically compares allometric methods in geometric morphometrics, distinguishing between two main schools of thought: one defining allometry as shape-size covariation (regression-based) and another as covariation among size-informed features (principal component-based).
Introduction to the Minimal Model Problem
Advanced studies in pure mathematics · 2018 · Q3 · 1,043 citations
This paper introduces the foundational concepts and conjectures within the Minimal Model Program (MMP), a major area of algebraic geometry focused on classifying algebraic varieties.
A Primer on Mapping Class Groups (PMS-49)
Princeton University Press eBooks · 2017 · FWCI 68.50 · 1,035 citations
This book provides a self-contained introduction to the mapping class group Mod(S), a central topic in geometry, topology, and group theory.
J-holomorphic curves and symplectic topology
2012 · FWCI 87.25 · 940 citations
This book rigorously establishes the fundamental theorems of J-holomorphic curves, a theory crucial for advancements in symplectic topology and mathematical physics.
Fixed points of a new type of contractive mappings in complete metric spaces
Fixed Point Theory and Applications · 2012 · Q3 · FWCI 23.76 · 912 citations · Open access
Researchers introduce a novel definition of contraction mappings and prove a fixed point theorem that generalizes the Banach contraction principle in a new way.
Elementary Differential Geometry
2018 · 877 citations
A summary is not available for this content.
Semilandmarks: a method for quantifying curves and surfaces
Bollettino del CILEA (CILEA) · 2013 · FWCI 48.40 · 852 citations
A new method called semilandmarks allows for the quantitative analysis of homologous curves and surfaces, expanding geometric morphometrics beyond traditional landmark coordinates.
HIDDEN ATTRACTORS IN DYNAMICAL SYSTEMS. FROM HIDDEN OSCILLATIONS IN HILBERT–KOLMOGOROV, AIZERMAN, AND KALMAN PROBLEMS TO HIDDEN CHAOTIC ATTRACTOR IN CHUA CIRCUITS
International Journal of Bifurcation and Chaos · 2013 · Q1 · FWCI 93.87 · 845 citations
This paper surveys efficient analytical-numerical methods for studying hidden attractors in nonlinear dynamical systems, which are distinct from self-excited attractors as their basins of attraction do not intersect with neighborhoods of equilibria.
Understanding Morphology
2013 · FWCI 17.52 · 787 citations
This revised edition of 'Understanding Morphology' offers a comprehensive introduction to word structure, incorporating the latest research and new pedagogical features.
geomorph: Software for geometric morphometric analyses
RUNE (Research UNE) · 2016 · 770 citations
The 'geomorph' software package is now freely available for geometric morphometric analyses of 2D and 3D landmark data within the R statistical environment.
P(0)2 Euclidean (Quantum) Field Theory
Princeton University Press eBooks · 2015 · FWCI 6.52 · 749 citations
This book introduces constructive quantum field theory through Euclidean methods, establishing deep connections between quantum fields and statistical mechanics of ferromagnets.
A field comes of age: geometric morphometrics in the 21 st century
Bollettino del CILEA (CILEA) · 2013 · FWCI 66.63 · 744 citations
Geometric morphometrics, a field that analyzes shape variation using landmark coordinates, has matured significantly over the past two decades, moving beyond simple distance measurements to a cohesive discipline.
The tps series of software
Bollettino del CILEA (CILEA) · 2015 · FWCI 72.20 · 678 citations
The 'tps' software series, designed for geometric morphometrics on Windows computers, has been widely adopted and utilized in numerous studies across various organisms.
Singularities of the Minimal Model Program
Cambridge University Press eBooks · 2013 · FWCI 20.12 · 672 citations
This book presents a comprehensive and self-contained theory of singularities arising in the Minimal Model Program (MMP) and moduli problems for algebraic varieties, including new unpublished results.
The Diophantine Equation 8<sup><i>x</i></sup> + <i>p</i><sup><i>y</i></sup> = <i>z</i><sup>2</sup>
The Scientific World JOURNAL · 2015 · Q2 · FWCI 140.13 · 672 citations · Open access
This paper proves that for a fixed odd prime p, the Diophantine equation 8^x + p^y = z^2 has no positive integer solutions when p is congruent to ±3 (mod 8).
Recently added
Portugaliae Mathematica
Portugaliae Mathematica · 2026 · Q4 · 404 citations
A specific class of surfaces of general type, characterized by K^2_S=8, p_g(S)=4, and q(S)=0, can be represented as a double cover of a quadric surface.
Contemporary Abstract Algebra
2025 · FWCI 3.27 · 460 citations
The Eleventh Edition of Contemporary Abstract Algebra enhances its classic approach with new exercises, examples, and applications, aiming to improve students' computational and proof-writing skills.
Advancing mathematics by guiding human intuition with AI
Nature · 2021 · Q1 · SJR 19.00 · FWCI 124.32 · 433 citations · Open access
Machine learning aided the discovery of new fundamental results in pure mathematics, including a novel connection between knot structures and a predicted algorithm for symmetric groups.
geomorph v4.0 and gmShiny: Enhanced analytics and a new graphical interface for a comprehensive morphometric experience
Methods in Ecology and Evolution · 2021 · Q1 · SJR 2.00 · FWCI 145.42 · 633 citations · Open access
The geomorph R package has been updated to v4.0, offering enhanced analytical capabilities and a new graphical user interface (gmShiny) for geometric morphometric analyses.
Generalized Complex Geometry
University lecture series · 2021 · FWCI 73.72 · 656 citations
Generalized complex geometry, encompassing complex and symplectic geometries, exhibits novel phenomena like B-field actions and applies to manifolds lacking standard complex/symplectic structures.
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