Exotic smooth structures on small 4-manifolds

DOI10.1007/s00222-008-0118-xzbMath1144.57026arXivmath/0701664OpenAlexW3098681389MaRDI QIDQ929369

B. Doug Park, Anar Akhmedov

Publication date: 17 June 2008

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701664

Mathematics Subject Classification ID

Related Items (21)

The Akhmedov-Park exotic \(\mathbb{CP}^2\# 3\overline{\mathbb{CP}}^2\) ⋮ The Akhmedov-Park exotic \(\mathbb{CP}^2\# 2\overline{\mathbb{CP}}^2\) ⋮ On the geography of simply connected nonspin symplectic 4-manifolds with nonnegative signature ⋮ Simply connected minimal symplectic 4-manifolds with signature less than \(-1\) ⋮ Exotic structures arising from fake projective planes ⋮ Topology. Abstracts from the workshop held July 24--30, 2022 ⋮ Complex ball quotients and new symplectic \(4\)-manifolds with nonnegative signatures ⋮ A symplectic manifold homeomorphic but not diffeomorphic to \(C\mathbb P^2 \# 3\overline{C\mathbb P}^2\) ⋮ Small exotic 4-manifolds and symplectic Calabi-Yau surfaces via genus-3 pencils ⋮ Genus \(2\) Lefschetz fibrations with \(b^+_2=1\) and \(c_1^2=1,2\) ⋮ Small exotic 4-manifolds from lines and quadrics in \(\mathbb{C}\mathbb{P}^2\) ⋮ Deformation of singular fibers of genus two fibrations and small exotic symplectic 4-manifolds ⋮ Exotic rational elliptic surfaces without 1-handles ⋮ Reverse engineering small 4-manifolds ⋮ Symplectic Calabi-Yau 6-manifolds ⋮ GEOGRAPHY AND BOTANY OF IRREDUCIBLE NON-SPIN SYMPLECTIC 4-MANIFOLDS WITH ABELIAN FUNDAMENTAL GROUP ⋮ Pinwheels and nullhomologous surgery on 4-manifolds with \(b^+=1\) ⋮ Small exotic rational surfaces without 1- and 3-handles ⋮ Exotic smooth structures on small 4-manifolds with odd signatures ⋮ New exotic 4-manifolds via Luttinger surgery on Lefschetz fibrations ⋮ Branched coverings of CP2 and other basic 4‐manifolds

Uses Software

• GAP

Cites Work

• Unnamed Item
• Unnamed Item
• On manifolds homeomorphic to \({\mathbb{C}}P^ 2\#8\overline{{\mathbb{C}}P}^ 2\)
• Exotic 4-manifolds with \(b_ 2^ + =1\)
• The topology of four-dimensional manifolds
• Exotic smooth structures on \(\mathbb {CP}^{2} \# 5 \overline{{\mathbb {CP}^2}}\)
• Complex versus differentiable classification of algebraic surfaces
• Irrationality and the h-cobordism conjecture
• On the diffeomorphism types of certain algebraic surfaces. I
• Knots, links, and 4-manifolds
• Rational blowdowns of smooth 4-manifolds
• Constructing infinitely many smooth structures on \(3\mathbb{CP}^2 \# n\overline{\mathbb{CP}}^2\)
• Simply connected symplectic 4-manifolds with \(b_2^+ = 1\) and \(c_1^2 = 2\)
• Knots.
• Monopoles and four-manifolds
• The Seiberg-Witten invariants and symplectic forms
• A new construction of symplectic manifolds
• Irreducible four-manifolds with small Euler characteristics
• A simply connected surface of general type with \(p_ g=0\)
• An exotic smooth structure on {\(\mathbb C\mathbb P^ 2\#6\overline{\mathbb C\mathbb P^ 2}\)}
• A symplectic manifold homeomorphic but not diffeomorphic to \(C\mathbb P^2 \# 3\overline{C\mathbb P}^2\)
• Reverse engineering small 4-manifolds
• Minimality and symplectic sums
• Exotic smooth structures on 3CP2♯8CP¯2
• Constructing infinitely many smooth structures on small 4-manifolds
• Shorter Notes: Some Simple Examples of Symplectic Manifolds
• Smoothly embedded spheres in symplectic 4-manifolds
• Seiberg-Witten invariants of generalised rational blow-downs
• Exotic smooth structures on $3\mathbf{CP}^2 # n\overline{\mathbf{CP}}^2$
• Exotic smooth structures on $3\mathbf{CP}^2 # n\overline{\mathbf{CP}}^2$, Part II
• Donaldson invariants of certain symplectic manifolds.
• Donaldson series and (-1)-tori.
• Minimality and irreducibility of symplectic four-manifolds
• SMALL EXOTIC 4-MANIFOLDS WITH ${\lowercase{B}}_2^+=3$
• Double node neighborhoods and families of simply connected 4-manifolds with 𝑏⁺=1
• Erratum

This page was built for publication: Exotic smooth structures on small 4-manifolds