The Burau estimate for the entropy of a braid

Algebraic and Geometric Topology

Volumn 7, Issue 1, 2007, Pages 1345-1378

  Band, Gavin ^a   Boyland, Philip ^b  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

^b UNIVERSITY OF FLORIDA   (United States)

Author keywords

Braid group; Burau representation; Dynamical systems

Indexed keywords

EID: 54749120527     PISSN: 14722747     EISSN: 14722739     Source Type: Journal    
DOI: 10.2140/agt.2007.7.1345     Document Type: Article

References (30)

1. R L Adler, A G Konheim, M H McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965) 309-319 MR0175106
2. E Artin, Theorie der zopfe, Abh. Math, Sem. Hamburg 4 (1925) 47-72
3. J S Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies 82, Princeton University Press (1974) MR0375281
4. J S Birman, T E Brendle, Braids: a survey, from: Handbook of knot theory, Elsevier B. V., Amsterdam (2005) 19-103 MR2179260
5. R Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971) 401-414 MR0274707
6. R Bowen, Entropy and the fundamental group, from: The structure of attractors in dynamical systems (Proc. Conf., North Dakota State Univ., Fargo, N.D., 1977), Lecture Notes in Math. 668, Springer (1978) 21-29 MR518545
7. P Boyland, Notes on dynamics of surface homeomorphisms, U. of Warwick Preprint Series (1989)
8. P Boyland, Topological methods in surface dynamics, Topology Appl. 58(3) (1994) 223-298 MR1288300
9. P Boyland, Isotopy stability of dynamics on surfaces, from: Geometry and topology in dynamics (WinstonSalem, NC, 1998/San Antonio, TX, 1999), Contemp. Math. 246, Amer. Math. Soc. (1999) 17-45 MR1732369
10. C Camacho, A Lins Neto, Geometric theory of foliations, Birkhäuser (1985) MR824240 Translated from the Portuguese by Sue E Goodman
11. M Denker, C Grillenberger, K Sigmund, Ergodic theory on compact spaces, Springer (1976) MR0457675 Lecture Notes in Mathematics, Vol. 527
12. A Fathi, F Laudenbach, V Poénaru, Travaux de Thurston sur les surfaces, Astérisque, Soci été Mathématique de France, Paris 66 (1979) Séminaire Orsay, with an English summary
13. R A Fenn, Techniques of geometric topology, London Mathematical Society Lecture Note Series 57, Cambridge University Press (1983) MR787801
14. J M Franks, Knots, links and symbolic dynamics, Ann. of Math. (2) 113 (1981) 529-552 MR621015
15. D Fried, Entropy and twisted cohomology, Topology 25 (1986) 455-470 MR862432
16. W Fulton, Algebraic topology, Graduate Texts in Mathematics 153, Springer (1995) MR1343250 A first course
17. E Gouillart, J L Thiffeault, M D Finn, Topological mixing with ghost rods, Phys. Rev. E (3) 73 (2006) MR2231368
18. A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications 54, Cambridge University Press (1995) MR1326374 With a supplementary chapter by Katok and Leonardo Mendoza
19. B P Kitchens, Symbolic dynamics, Universitext, Springer (1998) MR1484730 Onesided, twosided and countable state Markov shifts
20. B Kolev, Entropie topologique et représentation de Burau, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989) 835-838 MR1055205
21. A Manning, Topological entropy and the first homology group, Special Year in Dynamical Systems at Warwick University (1974) MR0650661
22. J W Milnor, Infinite cyclic coverings, from: Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967), Prindle, Weber & Schmidt, Boston (1968) 115-133 MR0242163
23. D Ruelle, D Sullivan, Currents, flows and diffeomorphisms, Topology 14(4) (1975) 319-327 MR0415679
24. E Rykken, Expanding factors for pseudo Anosov homeomorphisms, Michigan Math. J. 46(2) (1999) 281-296 MR1704217
25. S Schwartzman, Asymptotic cycles, Ann. of Math. (2) 66 (1957) 270-284 MR0088720
26. W T Song, K H Ko, J E Los, Entropies of braids, J. Knot Theory Ramifications 11 (2002) 647-666 MR1915500 Knots 2000 Korea, Vol. 2 (Yongpyong)
27. R G Swan, Projective modules over Laurent polynomial rings, Trans. Amer. Math. Soc. 237 (1978) 111-120 MR0469906
28. J L Thiffeault, Measuring topological chaos, Phys. Rev. Lett. 94(8) (2005)
29. J L Thiffeault, M D Finn, Topology, braids and mixing in fluids, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 364 (2006) 3251-3266 MR2317905
30. W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.) 19(2) (1988) 417-431 MR956596