ar X iv : 0 80 6 . 16 02 v 1 [ cs . C G ] 1 0 Ju n 20 08 The injectivity of the global function of a cellular automaton in the hyperbolic plane is undecidable

ar X iv : 0 80 6 . 27 19 v 1 [ m at h . G N ] 1 7 Ju n 20 08 A property of C p [ 0 , 1 ]

We prove that for every finite dimensional compact metric space X there is an open continuous linear surjection from Cp[0, 1] onto Cp(X). The proof makes use of embeddings introduced by Kolmogorov and Sternfeld in connection with Hilbert’s

On the injectivity of the global function of a cellular automaton in the hyperbolic plane (extended abstract)

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [5, 16, 7, 9] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem was answered positively in the case of the Euclidean plane by Jarkko Kari, in 1994, see [3]. In the present paper, we show that the answe...

Is the injectivity of the global function of a cellular automaton in the hyperbolic plane undecidable?

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [5,16,9,12] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem was answered positively in the case of the Euclidean plane by Jarkko Kari, in 1994, see [3]. In the present paper, we give a partial answer...

ar X iv : 0 80 6 . 46 34 v 1 [ he p - ex ] 3 0 Ju n 20 08 LPHE 2008 - 05 June 30 , 2008 B 0 – B 0 MIXING

ar X iv : 0 70 4 . 17 02 v 2 [ m at h . A G ] 2 6 Ju n 20 08 THE CANONICAL VOLUME OF 3 - FOLDS OF GENERAL TYPE WITH χ ≤ 0

We prove that the canonical volume K ≥ 1 30 for all 3-folds of general type with χ(O) ≤ 0. This bound is sharp.