Trisections and link surgeries

2019/09/30 by Kirby, Robion, Thompson, Abigail
#57M27 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1910.00086

Abstract

We examine questions about surgery on links which arise naturally from the trisection decomposition of 4-manifolds developed by Gay and Kirby. These links lie on Heegaard surfaces in #^j S¹ × S² and have surgeries yielding #^k S¹ × S². We describe families of links which have such surgeries. One can ask whether all links with such surgeries lie in these families; the answer is almost certainly no. We nevertheless give a small piece of evidence in favor of a positive answer.

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