2015/05/31 by Yuta Nozaki · 1 citation
Mathematics · #Algebraic geometry #Algebraic structures and combinatorial models #Boundary (topology) #Exact functor #Extension (predicate logic) #Functor #Functor category #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25 #msc:57M27
paper · pdf · doi:10.1007/s10711-016-0176-y
published in Geometriae Dedicata 185(1), 271-306 (Springer Science+Business Media) · 38 pages, many figures. The codomain of our functor and other minor errata have been fixed
arxiv created 2016/03/17 · openalex publication_date 2016/06/09 · openalex created_date 2016/06/24 · arxiv updated 2017/02/10 · openalex updated_date 2026/08/05
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.