Friedl, Stefan and Tillmann, Stephan (2020) TWO-GENERATOR ONE-RELATOR GROUPS AND MARKED POLYTOPES. ANNALES DE L INSTITUT FOURIER, 70 (2). pp. 831-879. ISSN 0373-0956, 1777-5310
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We use Fox calculus to assign a marked polytope to a "nice" group presentation with two generators and one relator. Relating the marked vertices to Novikov-Sikorav homology we show that they determine the Bieri-Neumann- Strebel invariant of the group. Furthermore we show that in most (possibly all) cases the marked polytope is an invariant of the underlying group and that in those cases the marked polytope also determines the minimal complexity of all the associated HNN-splittings.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GEOMETRIC INVARIANTS; THURSTON NORM; POLYNOMIALS; VALUATIONS; TORSION; THEOREM; Finitely presented group; Novikov ring; BNS invariant; Sigma invariant; Fox calculus |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Stefan Friedl |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Apr 2021 07:19 |
| Last Modified: | 07 Apr 2021 07:19 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45477 |
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