55 citations · 299 across the 25 of their papers we have counts for
26 papers · 1 filter
Indecomposable Klein bottles with order-4 meridians
Jeffrey Meier
We exhibit an infinite family of indecomposable Klein bottles in the 4-sphere with order-4 meridians.
Slice disks modulo local knotting
Jeffrey Meier, Allison N. Miller
The second author and Powell asked whether there exist knots bounding infinitely many slice disks that remain pairwise nonisotopic, even after local knotting. We answer this questi…
Knots bounding non-isotopic ribbon disks
Jeffrey Meier, Alexander Zupan
We exhibit infinitely many ribbon knots, each of which bounds infinitely many pairwise non-isotopic ribbon disks whose exteriors are diffeomorphic. This family provides a positive…
Bridge trisections and Seifert solids
Jason Joseph, Jeffrey Meier, Maggie Miller +1
We adapt Seifert's algorithm for classical knots and links to the setting of tri-plane diagrams for bridge trisected surfaces in the 4-sphere. Our approach allows for the construct…
Toric multisections and curves in rational surfaces
Gabriel Islambouli, Homayun Karimi, Peter Lambert-Cole +1
We study multisections of embedded surfaces in 4-manifolds admitting effective torus actions. We show that a simply-connected 4-manifold admits a genus one multisection if and only…
Bridge trisections and classical knotted surface theory
Jason Joseph, Jeffrey Meier, Maggie Miller +1
We seek to connect ideas in the theory of bridge trisections with other well-studied facets of classical knotted surface theory. First, we show how the normal Euler number can be c…
Filling braided links with trisected surfaces
Jeffrey Meier
We introduce the concept of a bridge trisection of a neatly embedded surface in a compact four-manifold, generalizing previous work with Alexander Zupan in the setting of closed su…
Cubic graphs induced by bridge trisections
Jeffrey Meier, Abigail Thompson, Alexander Zupan
Every embedded surface in the 4-sphere admits a bridge trisection, a decomposition of into three simple pieces. In this case, the surface $\mathca…
Symplectic 4-manifolds admit Weinstein trisections
Peter Lambert-Cole, Jeffrey Meier, Laura Starkston
We prove that every symplectic 4-manifold admits a trisection that is compatible with the symplectic structure in the sense that the symplectic form induces a Weinstein structure o…
Branched covers bounding rational homology balls
Paolo Aceto, Jeffrey Meier, Allison N. Miller +3
Prime power fold cyclic branched covers along smoothly slice knots all bound rational homology balls. This phenomenon, however, does not characterize slice knots. In this paper, we…
Null, recursively starlike-equivalent decompositions shrink
Jeffrey Meier, Patrick Orson, Arunima Ray
A subset of a metric space is said to be starlike-equivalent if it has a neighbourhood which is mapped homeomorphically into for some , sending to a s…
A note on three-fold branched covers of
Ryan Blair, Patricia Cahn, Alexandra Kjuchukova +1
We show that any 4-manifold admitting a -trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in , smoothly embedded except…
Generalized square knots and homotopy 4-spheres
Jeffrey Meier, Alexander Zupan
The purpose of this paper is to study geometrically simply-connected homotopy 4-spheres by analyzing -component links with a Dehn surgery realizing . We cal…
Bridge trisections in rational surfaces
Peter Lambert-Cole, Jeffrey Meier
We study smooth isotopy classes of complex curves in complex surfaces from the perspective of the theory of bridge trisections, with a special focus on curves in an…
Doubly pointed trisection diagrams and surgery on 2-knots
David Gay, Jeffrey Meier
We study embedded spheres in 4-manifolds (2-knots) via doubly pointed trisection diagrams, showing that such descriptions are unique up to stabilization and handleslides, and we de…
Bridge trisections of knotted surfaces in 4--manifolds
Jeffrey Meier, Alexander Zupan
We prove that every smoothly embedded surface in a 4--manifold can be isotoped to be in bridge position with respect to a given trisection of the ambient 4--manifold; that is, afte…
Trisections and spun 4-manifolds
Jeffrey Meier
We study trisections of 4-manifolds obtained by spinning and twist-spinning 3-manifolds, and we show that, given a (suitable) Heegaard diagram for the 3-manifold, one can perform s…
Characterizing Dehn surgeries on links via trisections
Jeffrey Meier, Alexander Zupan
We summarize and expand known connections between the study of Dehn surgery on links and the study of trisections of closed, smooth 4-manifolds. In addition, we describe how the po…
Bridge trisections of knotted surfaces in
Jeffrey Meier, Alexander Zupan
We introduce bridge trisections of knotted surfaces in the four-sphere. This description is inspired by the work of Gay and Kirby on trisections of four-manifolds and extends the c…
Classification of trisections and the Generalized Property R Conjecture
Jeffrey Meier, Trent Schirmer, Alexander Zupan
We show that the members of a large class of unbalanced four-manifold trisections are standard, and we present a family of trisections that is likely to include non-standard trisec…
A note on cabled slice knots and reducible surgeries
Jeffrey Meier
We consider the question of when a slice knot admits a reducible Dehn surgery. By analyzing the correction terms associated to such a surgery, we show that slice knots cannot admit…
Doubly slice knots with low crossing number
Charles Livingston, Jeffrey Meier
A knot in the three-sphere is doubly slice if it is the cross-section of an unknotted two-sphere in the four-sphere. For low-crossing knots, the most complete work to date gives a…
Genus two trisections are standard
Jeffrey Meier, Alexander Zupan
We show that the only closed 4-manifolds admitting genus two trisections are and connected sums of , , and $\overline{\mathbb{CP}}^2…
Fibered ribbon disks
Kyle Larson, Jeffrey Meier
We study the relationship between fibered ribbon 1-knots and fibered ribbon 2-knots by studying fibered slice disks with handlebody fibers. We give a characterization of fibered ho…