TL;DR
This paper extends the LMO functor to cobordisms with multiple boundary components, enhancing its ability to reflect relations among surface parts and connecting it to finite-type and Milnor invariants.
Contribution
It introduces a generalized LMO functor applicable to surfaces with any number of boundary components, broadening its theoretical scope.
Findings
Extended the LMO functor to multiple boundary components
Established relations with finite-type invariants
Linked the functor to Milnor invariants
Abstract
Cheptea, Habiro and Massuyeau constructed the LMO functor, which is defined on a certain category of cobordisms between two surfaces with at most one boundary component. In this paper, we extend the LMO functor to the case of any number of boundary components, and our functor reflects relations among the parts corresponding to the genera and boundary components of surfaces. We also discuss a relationship with finite-type invariants and Milnor invariants.
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