Corks, Plugs and exotic structures

Abstract

We discuss corks, and introduce new objects which we call plugs. Though plugs are fundamentally different objects, they also detect exotic smooth structures in 4-manifolds like corks. We discuss relation between corks, plugs and rational blow-downs. We show how to detect corks and plugs inside of some exotic manifolds. Furthermore, we construct knotted corks and plugs.

43 pages, 61 figures, published version

References in corpus (7)

• Akbulut's corks and h-cobordisms of smooth simply connected 4-manifolds
• A fake cusp and a fishtail
• Exotic rational elliptic surfaces without 1-handles
• The Dolgachev Surface
• Elliptic surfaces without 1-handles
• A note on Stein fillings of contact manifolds
• Small exotic Stein manifolds

Cited by in corpus (42)

• Stable isotopy in four dimensions
• Injectivity of satellite operators in knot concordance
• The Dolgachev Surface
• Nash homotopy spheres are standard
• Combinatorial properties of the K3 surface: Simplicial blowups and slicings
• On infinite order corks
• The geometry of the knot concordance space
• Knotting corks
• Stein 4-manifolds and corks
• Action of the cork twist on Floer homology
• Nuclei and exotic 4-manifolds
• Equivariant Corks
• The Catanese-Ciliberto-Mendes Lopes surface
• Quantum D-branes and exotic smooth R^4
• Infinitely many small exotic Stein fillings
• A construction of slice knots via annulus twists
• Twisting 4-manifolds along RP^2
• Constructing a quantum field theory from spacetime
• An infinite family of exotic Dolgachev surfaces without 1- and 3- handles
• Mazur manifolds and corks with small shadow complexities
• Simplicial blowups and discrete normal surfaces in simpcomp
• Heegaard Floer homology of Some Mazur Type Manifolds
• Corks with large shadow-complexity and exotic 4-manifolds
• Positive scalar curvature and $10/8$-type inequalities on $4$-manifolds with periodic ends
• Small exotic rational surfaces without 1- and 3-handles
• Mazur-type manifolds with $L$-space boundaries
• Gravitational sources induced by exotic smoothness
• Rational homology balls in $2$-handlebodies
• Nonexistence of twists and surgeries generating exotic 4-manifolds
• A note on Mazur type Stein fillings of planar contact manifolds
• Cork twists and automorphisms of $3$-manifolds
• Small exotic Stein manifolds
• Cork twisting exotic Stein 4-manifolds
• Abelian gerbes, generalized geometries and foliations of small exotic R^4
• Gluck twisting 4-manifolds with odd intersection form
• A cork of the rational surface with the second Betti number 9
• Infinite nonabelian corks
• Genus zero PALF structures on the Akbulut-Yasui plugs
• G-corks & Heegaard Floer Homology
• On instanton homology of corks W_n
• Nonexistence of Stein structures on 4-manifolds and maximal Thurston-Bennequin numbers
• Corks and automorphisms of 3-manifolds