Journal article
Thin position for knots, links, and graphs in 3-manifolds
Algebraic & geometric topology, Vol.18(3), pp.1361-1409
01/01/2018
DOI: 10.2140/agt.2018.18.1361
Abstract
We define a new notion of thin position for a graph in a 3-manifold which combines the ideas of thin position for manifolds first originated by Scharlemann and Thompson with the ideas of thin position for knots first originated by Gabai. This thin position has the property that connect-summing annuli and pairs-of-pants show up as thin levels. In a forthcoming paper, this new thin position allows us to define two new families of invariants of knots, links, and graphs in 3-manifolds. The invariants in one family are similar to bridge number, and the invariants in the other family are similar to Gabai's width for knots in the 3-sphere. The invariants in both families detect the unknot and are additive under connected sum and trivalent vertex sum.
Details
- Title: Subtitle
- Thin position for knots, links, and graphs in 3-manifolds
- Creators
- Scott A Taylor - Colby CollegeMaggy Tomova - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Algebraic & geometric topology, Vol.18(3), pp.1361-1409
- DOI
- 10.2140/agt.2018.18.1361
- ISSN
- 1472-2739
- eISSN
- 1472-2739
- Publisher
- GEOMETRY & TOPOLOGY PUBLICATIONS
- Number of pages
- 49
- Grant note
- Colby College Division of Natural Sciences NSF CAREER grant
- Language
- English
- Date published
- 01/01/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984241056802771
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