Legendrian singular links and singular connected sums
Byung Hee An, Youngjin Bae, Seonhwa Kim
TL;DR
This paper introduces the singular connected sum for Legendrian singular links, a new operation that generalizes the connected sum and aids in their classification within contact topology.
Contribution
It defines the singular connected sum for Legendrian singular links and explores phenomena unique to the Legendrian setting, advancing classification methods.
Findings
Defined the singular connected sum operation.
Provided classification techniques for Legendrian singular links.
Identified phenomena unique to Legendrian singular links.
Abstract
We study Legendrian singular links up to contact isotopy. Using a special property of the singular points, we define the singular connected sum of Legendrian singular links. This concept is a generalization of the connected sum and can be interpreted as a tangle replacement, which provides a way to classify Legendrian singular links. Moreover, we investigate several phenomena only occur in the Legendrian setup.
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