Just as it had after K1, low-dimensional topology advanced quickly following the release of K2. One major development was the elaboration of Seiberg-Witten theory, which used ideas from physics to distinguish between four-dimensional manifolds. By the late 2000s, the Kirby list was ready for updating again.<\/p>\n

\u201cThe thing is, the field became much bigger since the 1990s, it became huge,\u201d Baykur said.<\/p>\n

This time the impetus for creating a new list came from Ruberman and Baykur. They began collecting problems around 2013. But between their other obligations and the pandemic, it wasn\u2019t until October 2023 that they managed to gather a group of topologists to meet in person. They wanted the third version of the list to be more of a communal effort.<\/p>\n

\u201cThe initial list was wonderful, I\u2019m so glad it was there, but this new format is commendable in making that a bit more open,\u201d Ray said.<\/p>\n

In late 2022, Kirby joined Baykur and Ruberman as a co-organizer of the conference. They invited experts from the major areas of low-dimensional topology \u2014 corresponding to the same five-chapter structure Kirby had used in earlier versions of the list \u2014 but tried to avoid inviting so many specialists that no one had anything in common with anyone else.<\/p>\n

Baykur and Ruberman did most of the organizing while Kirby took on more of a titular role.<\/p>\n

\u201cIt\u2019s kind of like Rob\u2019s baby, you know, like he\u2019s emotionally in charge. But Danny and Inan\u00e7 handled all the logistics,\u201d Miller said.<\/p>\n

On Monday, October 30, the group began work on the K3 list (as it was called for obvious reasons and also in reference to K3 surfaces, which are important objects in topology).<\/p>\n

The list reflected ways in which low-dimensional topology had grown since K2. In the early 1990s the work of Andreas Floer gave rise to new methods for sorting three-dimensional manifolds. By the end of that decade those methods had blossomed into an entire area of study, Heegaard Floer homology, and within that area there are now a number of different approaches to distinguishing manifolds. Those approaches should all be consistent with each other, but it\u2019s not known for sure that they are, and K3 will include questions that aim to settle the matter.<\/p>\n<\/div>\n

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