Geometry and Topology papers

Pofolia’s corpus holds 73 papers from Geometry and Topology (2012–2026), each with a short summary. Below, the 20 most-cited, then the most recently added.

At a glance

• Most cited: Introduction: Motivation (2020, 2,278 citations).
• The 20 papers listed have 21,753 citations between them.
• 2 of the 6 with a known journal quartile appeared in a Q1 journal.
• 4 have a free full text (open access).
• Most frequent journals: Bollettino del CILEA (CILEA), Cambridge University Press eBooks, Princeton University Press eBooks.
• Published between 2012 and 2020.

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”. How to read the signals

• 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.

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• geomorph: anrpackage 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.

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• 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.

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• 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.

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• 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).

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• 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).

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• 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.

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• 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.

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• 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.

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• 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.

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• Elementary Differential Geometry

  2018 · 877 citations

  A summary is not available for this content.

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• The Diophantine Equation 8x + py = z2

  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).

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Recently added

• A filtered mapping cone formula for cables of the knot meridian

  Quantum Topology · 2026 · Q1 · 1 citations

  A new filtered mapping cone formula is developed to compute the knot Floer complex of (n,1)-cables of knot meridians in rational surgeries.

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• Toric vector bundles over a discrete valuation ring and Bruhat-Tits buildings

  Advances in Mathematics · 2026 · Q1 · SJR 2.00 · 1 citations

  A classification of rank r torus equivariant vector bundles on a toric scheme over a discrete valuation ring (O) is established, using graded piecewise linear maps to the building of GL(r).

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• Orthogonal dualities of dynamic stochastic higher spin vertex models, using the Drinfeld twister

  Journal of Physics A Mathematical and Theoretical · 2026 · Q2 · 1 citations · Open access

  A new algebraic method using the Drinfeld twister constructs duality functions for dynamic stochastic higher spin vertex models, proving they are 3φ2 functions.

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• Heegaard Floer homology and integer surgeries on links

  Geometry & Topology · 2025 · Q1 · SJR 3.00 · FWCI 6.28 · 56 citations · Open access

  A new framework, the 'complete system of hyperboxes', is introduced to describe the Heegaard Floer homology of integral surgeries on links within integral homology three-spheres.

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• 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.

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• 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.

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• 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.

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• 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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Journals in this field

The journals that publish most of this field’s papers. Quartile (Q1–Q4), SJR and h-index are from SCImago Journal Rank; “in this field” is how many of the journal’s pooled papers belong here. What is a Q1 journal? · What is the h-index?

Every journal in Geometry and Topology (Q1–Q4) →

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