Vol. 251, No. 1, 2011

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A note on the topology of the complements of fiber-type line arrangements in ℂℙ2

Sheng-Li Tan, Stephen S.-T. Yau and Fei Ye

Vol. 251 (2011), No. 1, 207–218
Abstract

We prove that BDiff+(S2,{x1,,xn+1}) is a K(π,1) space, where π is the mapping class group of an (n+1)-punctured sphere. As a consequence we derive that the center-projecting braid monodromy of a fiber-type projective line arrangement determines the diffeomorphic type of its complement.

Keywords
fiber-type line arrangement, braid monodromy, differentiable fiber bundle
Mathematical Subject Classification 2000
Primary: 14N20, 52C35
Secondary: 57R22, 37E30
Milestones
Received: 1 March 2010
Accepted: 1 July 2010
Published: 22 April 2011
Authors
Sheng-Li Tan
East China Normal University
Department of Mathematics
Shanghai 200062
China
http://math.ecnu.edu.cn/~sltan/intro.html
Stephen S.-T. Yau
University of Illinois at Chicago
Department of Mathematics, Statistics and Computer Science
322 SEO (m/c 249)
851 South Morgan Street
Chicago IL 60607
United States
http://www.math.uic.edu/~yau/
Fei Ye
University of Illinois at Chicago
Department of Mathematics, Statistics and Computer Science
322 SEO (m/c 249)
851 South Morgan Street
Chicago 60607
United States
http://www.math.uic.edu/~fye