Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Residual p Properties of Mapping Class Groups and Surface Groups

Luis Paris
Transactions of the American Mathematical Society
Vol. 361, No. 5 (May, 2009), pp. 2487-2507
Stable URL: http://www.jstor.org/stable/40302863
Page Count: 21
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Residual p Properties of Mapping Class Groups and Surface Groups
Preview not available

Abstract

Let . M(∑,P) be the mapping class group of a punctured oriented surface (∑P) (where P may be empty), and let $T_p (\Sigma ,{\rm{P}})$ be the kernel of the action of M(∑,P) on $H_1 (\Sigma \backslash {\rm{P}},F_p )$ We prove that $T_p (\Sigma ,{\rm P})$ is residually p. In particular, this shows that M(∑,P) is virtually residually p. For a group G we denote by $I_p (G)$ the kernel of the natural action of Out(G) on $H_1 (G,F_p ).$. In order to achieve our theorem, we prove that, under certain conditions (G is conjugacy p-separable and has Property A), the group $I_p (G)$ is residually p. The fact that free groups and surface groups have Property A is due to Grossman. The fact that free groups are conjugacy p-separable is due to Lyndon and Schupp. The fact that surface groups are conjugacy p-separable is, from a technical point of view, the main result of the paper.

Page Thumbnails

  • Thumbnail: Page 
2487
    2487
  • Thumbnail: Page 
2488
    2488
  • Thumbnail: Page 
2489
    2489
  • Thumbnail: Page 
2490
    2490
  • Thumbnail: Page 
2491
    2491
  • Thumbnail: Page 
2492
    2492
  • Thumbnail: Page 
2493
    2493
  • Thumbnail: Page 
2494
    2494
  • Thumbnail: Page 
2495
    2495
  • Thumbnail: Page 
2496
    2496
  • Thumbnail: Page 
2497
    2497
  • Thumbnail: Page 
2498
    2498
  • Thumbnail: Page 
2499
    2499
  • Thumbnail: Page 
2500
    2500
  • Thumbnail: Page 
2501
    2501
  • Thumbnail: Page 
2502
    2502
  • Thumbnail: Page 
2503
    2503
  • Thumbnail: Page 
2504
    2504
  • Thumbnail: Page 
2505
    2505
  • Thumbnail: Page 
2506
    2506
  • Thumbnail: Page 
2507
    2507