Journal article
TUNNEL NUMBER AND BRIDGE NUMBER OF COMPOSITE GENUS 2 SPATIAL GRAPHS
Pacific journal of mathematics, Vol.314(2), pp.451-494
10/01/2021
DOI: 10.2140/pjm.2021.314.451
Abstract
Connected sum and trivalent vertex sum are natural operations on genus 2 spatial graphs and, as with knots, tunnel number behaves in interesting ways under these operations. We prove sharp lower bounds on the degeneration of tunnel number under these operations. In particular, when the graphs are Brunnian theta-curves, we show that the tunnel number is bounded below by the number of prime factors and when the factors are m-small, then tunnel number is bounded below by the sum of the tunnel numbers of the factors. This extends theorems of Scharlemann-Schultens and Morimoto to genus 2 graphs. We are able to prove similar results for the bridge number of such graphs. The main tool is a family of recently defined invariants for knots, links, and spatial graphs that detect the unknot and are additive under connected sum and vertex sum. In this paper, we also show that they detect trivial theta-curves.
Details
- Title: Subtitle
- TUNNEL NUMBER AND BRIDGE NUMBER OF COMPOSITE GENUS 2 SPATIAL GRAPHS
- Creators
- Scott A Taylor - Colby CollegeMaggy Tomova - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Pacific journal of mathematics, Vol.314(2), pp.451-494
- DOI
- 10.2140/pjm.2021.314.451
- ISSN
- 0030-8730
- eISSN
- 1945-5844
- Publisher
- PACIFIC JOURNAL MATHEMATICS
- Number of pages
- 45
- Grant note
- NSF; National Science Foundation (NSF) Colby College
- Language
- English
- Date published
- 10/01/2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984241057202771
Metrics
21 Record Views