Maggie Miller

activity

20132026

most citedKnot cobordisms, bridge index, and torsion in Floer homology

22 citations · 100 across the 28 of their papers we have counts for

collaborators

30 papers

math.GT2026

Spanning solids and Murasugi sum in dimension four

Homayun Karimi, Seungwon Kim, Thomas Kindred +2

We study various constructions of spanning solids for knotted surfaces in the 4-sphere. In particular, we consider a 4-dimensional analogue of Murasugi sum, which we use to define…

math.GT2026

An irreducible real projective plane in the 4-sphere

Mark Hughes, Seungwon Kim, Maggie Miller +1

We construct an irreducible embedded projective plane in $S^{4}$ . This gives a counterexample to the Kinoshita conjecture and answers Problem 4.37 of the K3 problem list. Moreover, w…

math.GT2023

Non-isotopic splitting spheres for a split link in $S^{4}$

Mark Hughes, Seungwon Kim, Maggie Miller

We show that there exist split, orientable, 2-component surface-links in $S^{4}$ with non-isotopic splitting spheres in their complements. In particular, for non-negative integers $m…

math.GT2023

Explicitly describing fibered 3-manifolds through families of singularly fibered surfaces

Maggie Miller

We give an explicit description of a fibration of the complement of the closure of a homogeneous braid, understanding how each fiber intersects every cross-section of $S^{3}$ .

math.GT2023★ 1 cited

Slice obstructions from genus bounds in definite 4-manifolds

Paolo Aceto, Nickolas A. Castro, Maggie Miller +2

We discuss an obstruction to a knot being smoothly slice that comes from minimum-genus bounds on smoothly embedded surfaces in definite 4-manifolds. As an example, we provide an al…

math.GT2022

Concordance of spheres in 4-manifolds with an immersed dual sphere

Michael Klug, Maggie Miller

Let $S_{0}$ and $S_{1}$ be two homotopic, oriented 2-spheres embedded in an orientable 4-manifold $X$ . After discussing several operations for modifying an immersion of a 3-manifold in…

math.GT2022

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…

math.GT2022

Seifert surfaces in the 4-ball

Kyle Hayden, Seungwon Kim, Maggie Miller +2

We answer a question of Livingston from 1982 by producing Seifert surfaces of the same genus for a knot in $S^{3}$ that do not become isotopic when their interiors are pushed into $B…

math.GT2021★ 2 cited

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…

math.GT2021

Knotted handlebodies in the 4-sphere and 5-ball

Mark Hughes, Seungwon Kim, Maggie Miller

For every integer $g \geq 2$ we construct 3-dimensional genus- $g$ 1-handlebodies smoothly embedded in $S^{4}$ with the same boundary, and which are defined by the same cut systems of t…

math.GT2021

Band diagrams of immersed surfaces in 4-manifolds

Mark Hughes, Seungwon Kim, Maggie Miller

We study immersed surfaces in smooth 4-manifolds via singular banded unlink diagrams. Such a diagram consists of a singular link with bands inside a Kirby diagram of the ambient 4-…

math.GT2021

Brunnian exotic surface links in the 4-ball

Kyle Hayden, Alexandra Kjuchukova, Siddhi Krishna +3

This paper investigates the exotic phenomena exhibited by links of disconnected surfaces with boundary that are properly embedded in the 4-ball. Our main results provide two differ…

math.GT2020★ 6 cited

Lefschetz fibrations on nonorientable 4-manifolds

Maggie Miller, Burak Ozbagci

Let $W$ be a nonorientable $4$ -dimensional handlebody without $3$ - and $4$ -handles. We show that $W$ admits a Lefschetz fibration over the $2$ -disk, whose regular fiber is a nonori…

math.GT2020

Trisections of non-orientable 4-manifolds

Maggie Miller, Patrick Naylor

We study trisections of smooth, compact non-orientable 4-manifolds, and introduce trisections of non-orientable 4-manifolds with boundary. In particular, we prove a non-orientable…

math.GT2020

Equivalent characterizations of handle-ribbon knots

Maggie Miller, Alexander Zupan

The stable Kauffman conjecture posits that a knot in $S^{3}$ is slice if and only if it admits a slice derivative. We prove a related statement: A knot is handle-ribbon (also called…

math.GT2020★ 6 cited

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…

math.GT2020★ 7 cited

Transverse invariants and exotic surfaces in the 4-ball

András Juhász, Maggie Miller, Ian Zemke

Using 1-twist rim surgery, we construct infinitely many smoothly embedded, orientable surfaces in the 4-ball bounding a knot in the 3-sphere that are pairwise topologically isotopi…

math.GT2019★ 2 cited

Concordance of Surfaces and the Freedman-Quinn Invariant

Michael R. Klug, Maggie Miller

We prove a concordance version of the 4-dimensional light bulb theorem for $π_{1}$ -negligible compact orientable surfaces, where there is a framed but not necessarily embedded dual s…

math.GT2019★ 10 cited

The relative $L$ -invariant of a compact $4$ -manifold

Nickolas A. Castro, Gabriel Islambouli, Maggie Miller +1

In this paper, we introduce the relative $L$ -invariant $r L (X)$ of a smooth, orientable, compact 4-manifold $X$ with boundary. This invariant is defined by measu…

math.GT2019★ 2 cited

The 0-concordance monoid admits an infinite linearly independent set

Irving Dai, Maggie Miller

Under the relation of $0$ -concordance, the set of knotted 2-spheres in $S^{4}$ forms a commutative monoid $M_{0}$ with the operation of connected sum. Sunukjian has recently…

math.GT2019

The effect of link Dehn surgery on the Thurston norm

Maggie Miller

Let $L$ be an $n$ -component link ( $n > 1$ ) with pairwise nonzero linking numbers in a rational homology $3$ -sphere $Y$ . Assume the link complement $X := Y ∖ ν (L)$ has nondegenera…

math.GT2019

Trisections of 5-manifolds

Peter Lambert-Cole, Maggie Miller

Gay and Kirby introduced the notion of a trisection of a smooth 4-manifold, which is a decomposition of the 4-manifold into three elementary pieces. Rubinstein and Tillmann later e…

math.GT2019★ 22 cited

Knot cobordisms, bridge index, and torsion in Floer homology

András Juhász, Maggie Miller, Ian Zemke

Given a connected cobordism between two knots in the 3-sphere, our main result is an inequality involving torsion orders of the knot Floer homology of the knots, and the number of…

math.GT2019★ 3 cited

A concordance analogue of the $4$ -dimensional light bulb theorem

Maggie Miller

We prove a concordance analogue of Gabai's $4$ -dimensional light bulb theorem. That is, we show that when $R$ and $R^{'}$ are homotopically (smoothly) embedded $2$ -spheres in a $4$ -ma…

Spanning solids and Murasugi sum in dimension four

An irreducible real projective plane in the 4-sphere

Non-isotopic splitting spheres for a split link in S4

Explicitly describing fibered 3-manifolds through families of singularly fibered surfaces

Slice obstructions from genus bounds in definite 4-manifolds

Concordance of spheres in 4-manifolds with an immersed dual sphere

Bridge trisections and Seifert solids

Seifert surfaces in the 4-ball

Bridge trisections and classical knotted surface theory

Knotted handlebodies in the 4-sphere and 5-ball

Band diagrams of immersed surfaces in 4-manifolds

Brunnian exotic surface links in the 4-ball

Lefschetz fibrations on nonorientable 4-manifolds

Trisections of non-orientable 4-manifolds

Equivalent characterizations of handle-ribbon knots

Branched covers bounding rational homology balls

Transverse invariants and exotic surfaces in the 4-ball

Concordance of Surfaces and the Freedman-Quinn Invariant

The relative L-invariant of a compact 4-manifold

The 0-concordance monoid admits an infinite linearly independent set

The effect of link Dehn surgery on the Thurston norm

Trisections of 5-manifolds

Knot cobordisms, bridge index, and torsion in Floer homology

A concordance analogue of the 4-dimensional light bulb theorem

Non-isotopic splitting spheres for a split link in $S^{4}$

The relative $L$ -invariant of a compact $4$ -manifold

A concordance analogue of the $4$ -dimensional light bulb theorem