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Diagrams for Relative Trisections

- N. A. Castro, David T. Gay, Juanita Pinz'on-Caicedo
- Mathematics
- 20 October 2016

We establish a correspondence between trisections of smooth, compact, oriented $4$--manifolds with connected boundary and diagrams describing these trisected $4$--manifolds. Such a diagram comes in… Expand

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Framed instanton homology of surgeries on L-space knots

- Tye Lidman, Juanita Pinz'on-Caicedo, C. Scaduto
- Mathematics
- 6 March 2020

An important class of three-manifolds are L-spaces, which are rational homology spheres with the smallest possible Floer homology. For knots with an instanton L-space surgery, we compute the framed… Expand

8 2- PDF

Trisections of 4-manifolds with boundary

- N. A. Castro, David T. Gay, Juanita Pinz'on-Caicedo
- Mathematics, Medicine
- Proceedings of the National Academy of Sciences
- 26 January 2018

Significance Trisections are decompositions of 4D spaces (4-manifolds) into three pieces; these decompositions become both richer and more subtle when the 4-manifolds have 3D boundaries and even more… Expand

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A note on the topological slice genus of satellite knots

- P. Feller, Allison N. Miller, Juanita Pinz'on-Caicedo
- Mathematics
- 10 August 2019

This paper presents evidence supporting the surprising conjecture that in the topological category the slice genus of a satellite knot $P(K)$ is bounded above by the sum of the slice genera of $K$… Expand

5 1- PDF

Toroidal homology spheres and SU(2)-representations

- Tye Lidman, Juanita Pinz'on-Caicedo, Raphael Zentner
- Mathematics
- 7 January 2021

We prove that if an integer homology three-sphere contains an embedded incompressible torus, then its fundamental group admits irreducible SU(2)representations. Our methods use instanton Floer… Expand

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Four–manifolds and knot concordance

Topology deals with global or large-scale structures of objects. Geometric topology is the study of manifolds and its ultimate goal is the classification of manifolds within a certain framework… Expand

Satellites of Infinite Rank in the Smooth Concordance Group

- M. Hedden, Juanita Pinz'on-Caicedo
- Mathematics
- 11 September 2018

We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use $SO(3)$… Expand

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Independence of Satellites of Torus Knots in the Smooth Concordance Group

- Juanita Pinz'on-Caicedo
- Mathematics
- 14 January 2015

The main goal of this article is to obtain a condition under which an infinite collection $\mathscr{F}$ of satellite knots (with companion a positive torus knot and pattern similar to the Whitehead… Expand

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Independence of Iterated Whitehead Doubles

- Juanita Pinz'on-Caicedo
- Mathematics
- 14 December 2017

A theorem of Furuta and Fintushel-Stern provides a criterion for a collection of Seifert fibred homology spheres to be independent in the homology cobordism group of oriented homology 3-spheres. In… Expand

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Traceless SU(2) representations of 2-stranded tangles

- Y. Fukumoto, P. Kirk, Juanita Pinz'on-Caicedo
- Mathematics
- Mathematical Proceedings of the Cambridge…
- 26 May 2013

Abstract Given a 2-stranded tangle T contained in a ℤ-homology ball Y, we investigate the character variety R(Y, T) of conjugacy classes of traceless SU(2) representations of π1(Y \ T). In particular… Expand

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