Arunima Ray

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math.GT2026

Triangulating Spun 2-Knot Complements

Rhuaidi Antonio Burke, Benjamin Burton, Arunima Ray +3

A $2$ -knot is an embedding of a $2$ -sphere into the $4$ -sphere. Similar to the case of embedding circles into the $3$ -sphere, this allows the $2$ -sphere to be knotted. In this shor…

math.GT2025

Constructing locally flat surfaces in 4-manifolds

Arunima Ray

There are two main approaches to building locally flat embedded surfaces in 4-manifolds: direct methods which geometrically manipulate a given map of a surface, and more indirect m…

math.GT2025

Not all knots are smoothly round handle slice

Tye Lidman, Allison N. Miller, Arunima Ray

Freedman and Krushkal showed that if the surgery conjecture and the $s$ -cobordism conjecture hold for all topological 4-manifolds, then every link with pairwise zero linking number…

math.GT2024

A note on surfaces in $CP^{2}$ and $CP^{2} # CP^{2}$

Marco Marengon, Allison N. Miller, Arunima Ray +1

In this brief note, we investigate the $CP^{2}$ -genus of knots, i.e. the least genus of a smooth, compact, orientable surface in $CP^{2} ∖ B^{4} ˚$ boun…

Triangulating Spun 2-Knot Complements

Constructing locally flat surfaces in 4-manifolds

Not all knots are smoothly round handle slice

A note on surfaces in CP2 and CP2#CP2

A note on surfaces in $CP^{2}$ and $CP^{2} # CP^{2}$