Abstract
It is well-known that every 3-manifold M3 may be represented by a framed link (L,c), which indicates the Dehn-surgery from [Formula: see text] to M3 = M3(L,c); moreover, M3 is the boundary of a PL 4-manifold M4 = M4(L, c), which is obtained from [Formula: see text] by adding 2-handles along the framed link (L, c). In this paper we study the relationships between the above representations and the representation theory of general PL-manifolds by edge-coloured graphs: in particular, we describe how to construct a 5-coloured graph representing M4=M4(L,c), directly from a planar diagram of (L,c). As a consequence, relations between the combinatorial properties of the link L and both the Heegaard genus of M3=M3(L,c) and the regular genus of M4=M4(L,c) are obtained.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
