# The diffeomorphism group of a K3 surface and Nielsen realization

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Let G be a (2, m, n)-group and let x be the number of distinct primes dividing Ï‡, the Euler characteristic of G. We prove first that, apart from a finite number of known exceptions, a non-abelian simple composition factor T of G is a finite group of Lie type with rank n â‰¤ x. This...

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No abstract available.

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This is an announcement of the results in the paper [4] which is one of the series of papers dealing with the existence of spun normal surfaces in 3-manifolds with ideal triangulations. We give short comments for proofs of the results without details.

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In this paper, we apply the theory of Chern-Cheeger-Simons to construct canonical invariants associated to an r-simplex whose points parametrize flat connections on a smooth manifold X. These invariants lie in degrees (2 p âˆ’ r âˆ’ 1)-cohomology with $${\mathbb{C}/\mathbb{Z}}$$...

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Given a class C of subgroups of a topological group G, we say that a subgroup H âˆˆ C is a universal C subgroup of G if every subgroup K âˆˆ C is a continuous homomorphic preimage of H. Such subgroups may be regarded as complete members of C with respect to a natural preorder on the set of...