An operad of 3-manifolds
@inproceedings{Femi2021AnOO,
title={An operad of 3-manifolds},
author={Bojana Femi{\'c} and Vladimir Grujic and Jovan Obradovic and Zoran Petric},
year={2021}
}A coloured operad whose operadic operations are 3-cobordisms is introduced in this paper. This operad is presented purely combinatorially through diagrams in handlebodies together with a calculus, which is a generalization of Kirby’s calculus. Both integral and rational calculi are developed and a calculus consisting of finite set of local moves is presented in the paper. Mathematics Subject Classification (2010): 18D50, 57M25, 57M27
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References
SHOWING 1-10 OF 13 REFERENCES
Kirby calculus in manifolds with boundary
- Mathematics
- 1997
Suppose there are two framed links in a compact, connected 3-manifold (possibly with boundary, or non-orientable) such that the associated 3-manifolds obtained by surgery are homeomorphic (relative…
A finite set of local moves for Kirby calculus
- Mathematics
- 2011
We exhibit a finite set of local moves that connect any two surgery presentations of the same 3-manifold via framed links in the three-sphere. The moves are handle-slides and blow-downs/ups of a…
A Representation of Orientable Combinatorial 3-Manifolds
- Mathematics
- 1962
The following question has been posed by Bing [1]: "Which compact, connected 3-manifolds can be obtained from S3 as follows: Remove a finite collection of mutually exclusive (but perhaps knotted and…
Bridged Links and Tangle Presentations of Cobordism Categories
- Mathematics
- 1998
Abstract We develop a calculus of surgery data, called bridged links , which involves besides links also pairs of balls that describe one-handle attachments. As opposed to the usual link calculi of…
Three-Dimensional 2-Framed TQFTs and Surgery
- Mathematics
- 1999
The notion of 2-framed three-manifolds is defined. The category of 2-framed cobordisms is described, and used to define a 2-framed three-dimensional TQFT. Using skeletonization and special features…
Notes on Basic 3-Manifold Topology
- Mathematics
- 2001
These notes, originally written in the 1980’s, were intended as the beginning of a book on 3 manifolds, but unfortunately that project has not progressed very far since then. A few small revisions…
Notes on Heegaard splittings
- 2007
Sosinskiȋ, Knots, Links, Braids and 3-Manifolds
- Translations of Mathematical Monographs
- 1996