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Detecting L-spaces among branched covers of L-space knots

Lead Research Organisation: UNIVERSITY OF CAMBRIDGE
Department Name: Pure Maths and Mathematical Statistics

Abstract

I am working in the area of geometry and topology. More precisely, I am working on knot theory; a field in interplay of topology, geometry and algebraic geometry. In my project I am interested in finding if (and under what conditions) a branched cover of an L-space knot is an L-space and, more generally, answering the L-space conjecture for these spaces. I am using bordered Floer theory of Hanselman-Rasmussen-Watson to answer these questions. Moreover, I am thinking about establishing relations between the said Floer theory and gauge theories like Seiberg-Witten theory or instanton Floer theory.

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