ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 57, 55, 22 Tsuboi, Takashi, University of Tokyo, Japan On the group of area preserving homeomorphisms Let Homeo_{Ω}^{L}(D^{2}) denote the group of orientation preserving and area preserving Lipschitz homeomorphisms of the 2-disk D^{2}. Let Homeo^{L}(S^{1})_{0} denotes the group of orientation preserving Lipschitz homeomorphisms of the circle S^{1} = ∂D^{2}. Let Homeo_{Ω}^{L}(D^{2}, ∂D^{2}) denote the kernel of the restriction homomorphism Homeo_{Ω}^{L}(D^{2}) ⟶ Homeo^{L}(S^{1})_{0}. One can define the Calabi invariant Homeo_{Ω}^{L}(D^{2}, ∂D^{2}) ⟶ R and we show a relationship between the Euler class in the group cohomology of Homeo^{L}(S^{1})_{0} and the Calabi invariant, generalizing our previous result for the corresponding groups of diffeomorphisms. We also give some application to the group of piecewise linear homeomorphisms. Reference: T. Tsuboi, The Calabi invariant and the Euler class, to appear in Transactions Amer. Math. Soc.