The minimal genus problem -- a quarter century of progress

DOI10.1007/s10473-022-0604-zOpenAlexW4293561624MaRDI QIDQ2080971

Josef G. Dorfmeister, Tian-Jun Li

Publication date: 12 October 2022

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10473-022-0604-z

zbMATH Keywords

minimal genusfour manifoldsadjunction-type inequalitycircle sum

Mathematics Subject Classification ID

Cites Work

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• Minimal genera of open 4-manifolds
• Positive 2-spheres in 4-manifolds of signature \((1,n)\)
• Symplectic genus, minimal genus and diffeomorphisms
• Two-dimensional submanifolds of four-dimensional manifolds
• Classification of certain pairs of operators (P,Q) satisfying \([P,Q=- iId\)]
• The minimal genus problem in rational surfaces \(CP^2 \sharp n\overline{CP^2}\)
• Symmetry of Reidemeister torsion on \(SU_2\)-representation spaces of knots
• On diffeomorphism types of certain algebraic surfaces. II
• Smooth embeddings of 2-spheres in 4-manifolds
• Minimal genus in \(S^1\times M^3\)
• On the diffeomorphism groups of elliptic surfaces
• The minimal genus problem
• Minimal genus smooth embeddings in \(S^2\times S^2\) and \(CP^2\# n\overline{CP^2}\) with \(n\leq 8\)
• Smooth minimal genera for small negative classes in \({\mathbb C}P^{2}{\#}n{\overline{{\mathbb C}P}^2}\) with \(n {\leqslant} 9\)
• Higher type adjunction inequalities in Seiberg-Witten theory
• Stability and existence of surfaces in symplectic 4-manifolds with \(b^+=1\)
• Genus inequalities and four-dimensional surgery
• Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary
• Bounds on genus and geometric intersections from cylindrical end moduli spaces
• Symplectic structure on ruled surfaces and a generalized adjunction formula
• The symplectic Thom conjecture
• Bridge trisections in \(\mathbb{CP}^2\) and the Thom conjecture
• The minimal genus problem for elliptic surfaces
• Minimal genus problem for \(T^2\)-bundles over surfaces
• Trisections, intersection forms and the Torelli group
• Nonorientable surfaces in homology cobordisms (with an appendix by Ira M. Gessel)
• The minimal genus problem in \(\mathbb{CP}^2\# \mathbb{CP}^2\)
• Minimal genus in 4-manifolds with a free circle action
• On the diffeomorphism groups of rational and ruled 4-manifolds
• Minimal genus for 4-manifolds withb⁺ = 1
• Minimal genus in circle bundles over 3-manifolds
• Homology classes of negative square and embedded surfaces in 4-manifolds
• Homotopy theoretical considerations of the Bauer-Furuta stable homotopy Seiberg-Witten invariants
• THE MINIMAL GENUS PROBLEM IN RULED MANIFOLDS
• Generalization of the Whitney-Mahowald Theorem
• Representing homology classes by locally flat surfaces of minimum genus
• Tori in certain aspherical four-manifolds
• Representing nonnegative homology classes of ℂℙ²#𝕟\overline{ℂℙ}² by minimal genus smooth embeddings
• Bounds on genus and configurations of embedded surfaces in 4-manifolds
• Circle-sum and minimal genus surfaces in ruled 4-manifolds
• Diffeomorphisms of 4-Manifolds