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The homology homomorphism induced by Harer map

송용진|이덕주
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2011.12|한국수학논문집 (Korean Journal of Mathematics)|제19권 제4호|pp. 409-421

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참고문헌

키워드

braid groupsautomorphism groups of groupsmapping class groups
주제분류수학

초록

We study a natural map from the braid group to the mapping class group which is called Harer map. It is rather new and different from the classical map which was studied in 1980's by F. Cohen, J. Harer et al. We show that this map is homologically trivial for most coefficients by using the fact that this map factors through the symmetric group.

Abstract

We study a natural map from the braid group to the mapping class group which is called Harer map. It is rather new and different from the classical map which was studied in 1980's by F. Cohen, J. Harer et al. We show that this map is homologically trivial for most coefficients by using the fact that this map factors through the symmetric group.

참고문헌 (13)

  1. E. Artin, "Theorie der Zopfe", Abh. Math. Sem. Univ. Hamburg, 4, pp.47~72 (1926)
  2. C. F. B¨odigheimer, "Stripping and splitting decorated mapping class groups, Cohomological methods in homotopy theory (Bellaterra, 1998)", Progr. Math, 196, pp.47~57 (2001), Birkhauser, Basel
  3. F. R. Cohen, "The homology of iterated loop space, Lecture Notes in Mathematics 533" (1976), Springer-Verlag
  4. S. Galatius, "Stable homology of automorphism groups of free groups", Ann. of Math, 173(2), pp.705~768 (2011)
  5. J. Harer, "Stability of the homology of the mapping class groups of orientable surfaces", Ann. of Math, 121(2), pp.215~249 (1985)
  6. A. Hatcher, "Cerf theory for graphs", J. London Math. Soc, 52(2), pp.633~655 (1998)
  7. A. Hatcher, "Homology stability for outer automorphism groups of free groups", Algebr. Geom. Topol, 4, pp.1253~1272 (2004)
  8. N. V. Ivanov, "Stabilization of the homology of Teichmuller modular groups, Algebra i Analiz 1 (3) (1989), 110–126", Leningrad Math. J, 3(1), pp.675~691 (1990)
  9. M. Nakaoka, "Decomposition theorem for homology groups of symmetric groups", Ann. of Math, 71(2), pp.16~42 (1960)
  10. J. Powell, "Two theorems on the mapping class group of a surface", Proc. Amer. Math. Soc, 68(3), pp.347~350 (1978)
  11. G. Segal, "Configuration spaces and iterated loop spaces", Invent. Math, 21, pp.213~221 (1973)
  12. U. Tillmann, "Artin's map in stable homology", Bull. Lond. Math. Soc, 39(6), pp.989~992 (2007)
  13. J. B. Wagoner, "Delooping classifying spaces in algebraic K-theory", Topology, 11, pp.349~371 (1972)

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