Algebraic & Geometric Topology

On a question of Etnyre and Van Horn-Morris

Tetsuya Ito and Keiko Kawamuro

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at msp.org/agt.

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The purpose of this note is to answer Question 6.12 of Etnyre and Van Horn-Morris [Monoids in the mapping class group, Geom. Topol. Monographs 19 (2015) 319–365], asking when the set of mapping classes whose fractional Dehn twist coefficient is greater than a given constant forms a monoid.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 1 (2017), 561-566.

Dates
Received: 4 May 2016
Revised: 16 May 2016
Accepted: 6 June 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841321

Digital Object Identifier
doi:10.2140/agt.2017.17.561

Mathematical Reviews number (MathSciNet)
MR3604385

Zentralblatt MATH identifier
1360.57010

Subjects
Primary: 57M07: Topological methods in group theory
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

Keywords
Fractional Dehn twist coefficient monoid mapping class group

Citation

Ito, Tetsuya; Kawamuro, Keiko. On a question of Etnyre and Van Horn-Morris. Algebr. Geom. Topol. 17 (2017), no. 1, 561--566. doi:10.2140/agt.2017.17.561. https://projecteuclid.org/euclid.agt/1510841321


Export citation

References

  • M Bestvina, K Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002) 69–89
  • J,B Etnyre, J Van Horn-Morris, Monoids in the mapping class group, from “Interactions between low-dimensional topology and mapping class groups” (R,I Baykur, J,B Etnyre, U Hamenstädt, editors), Geom. Topol. Monographs 19 (2015) 319–365
  • B Farb, D Margalit, A primer on mapping class groups, Princeton Mathematical Series 49, Princeton University Press (2012)
  • K Honda, W,H Kazez, G Matić, Right-veering diffeomorphisms of compact surfaces with boundary, Invent. Math. 169 (2007) 427–449
  • T Ito, K Kawamuro, Visualizing overtwisted discs in open books, Publ. Res. Inst. Math. Sci. 50 (2014) 169–180
  • T Ito, K Kawamuro, Overtwisted discs in planar open books, Internat. J. Math. 26 (2015) art. ID 1550027
  • T Ito, K Kawamuro, Essential open book foliation and fractional Dehn twist coefficient, Geom. Dedicata (online publication August 2016)
  • A Wand, Detecting tightness via open book decompositions, from “Interactions between low-dimensional topology and mapping class groups” (R,I Baykur, J,B Etnyre, U Hamenstädt, editors), Geom. Topol. Monographs 19 (2015) 291–317