## Geometry & Topology

### The symmetry of intersection numbers in group theory

Peter Scott

#### Abstract

For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.

#### Article information

Source
Geom. Topol., Volume 2, Number 1 (1998), 11-29.

Dates
Received: 21 February 1997
Revised: 13 March 1998
Accepted: 19 March 1998
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513882900

Digital Object Identifier
doi:10.2140/gt.1998.2.11

Mathematical Reviews number (MathSciNet)
MR1608688

Zentralblatt MATH identifier
0897.20029

#### Citation

Scott, Peter. The symmetry of intersection numbers in group theory. Geom. Topol. 2 (1998), no. 1, 11--29. doi:10.2140/gt.1998.2.11. https://projecteuclid.org/euclid.gt/1513882900

#### References

• D E Cohen, Groups of cohomological dimension one, Lecture Notes in Math. 245, Springer–Verlag, Berlin (1972)
• M Dunwoody, M Sageev, JSJ splittings for finitely presented groups over slender groups, preprint
• M H Freedman, J Hass, P Scott, Closed geodesics on surfaces, Bull. London Math. Soc. 14 (1982) 385–391
• M H Freedman, J Hass, P Scott, Least area incompressible surfaces in 3–manifolds, Invent. Math. 71 (1983) 609–642.
• C H Houghton, Ends of locally compact groups and their quotient spaces, J. Aust. Math. Soc. 17 (1974) 274–284
• P H Kropholler, M A Roller, Splittings of Poincaré duality groups, Math. Zeit. 197 (1988) no. 3, 421–438
• E Rips, Z Sela, Cyclic splittings of finitelypresented groups and the canonical JSJ decomposition, preprint
• P Scott, Ends of pairs of groups, J. Pure Appl. Algebra 11 (1977) 179–198
• P Scott, A new proof of the Annulus and Torus Theorems, Amer. J. Math. 102 (1980) 241–277
• P Scott, G A Swarup, An Algebraic Annulus Theorem, preprint
• P Scott, C T C Wall, Topological methods in group theory, from: “Homological Group Theory”, London Math. Soc. Lecture Notes Series 36 (1979) 137–214
• J-P Serre, Arbres, amalgames, $SL_{2}$, Astérisque No. 46, Société Mathématique de France, Paris (1977)
• J-P Serre, Trees, translated from French by John Stillwell, Springer–Verlag, Berlin–New York (1980) ISBN 3-540-10103-9