A pr 2 00 4 WORD MAPS HAVE LARGE IMAGE
نویسنده
چکیده
An element w in the free group on r letters defines a map fw,G: G r → G for each group G. In this note, we show that whenever w 6= 1 and G is a semisimple algebraic group, fw,G is dominant. As an application, we show that for fixed w and Γi a sequence of pairwise non-isomorphic finite simple groups, lim i→∞ log |Γi| log |f w,Γi (Γ r i )| = 1. Let Fr be the free group on r generators x1, . . . , xr. For any group G, each word w = x1 a1x b2 a2 · · ·xm am ∈ Fr defines a corresponding word map fw,G: G r → G: fw,G(g1, . . . , gr) = g b1 a1 g2 a2 · · · g bm am . The main result of this note is as follows: Theorem 1: If G is a simple algebraic group over any field K and w 6= 1, then fw,G is a dominant morphism. In other words, fw,G(G) contains a non-trivial Zariski-open subset of G. As an application, we prove the following theorem, which answers a question of A. Shalev: * Partially supported by NSF Grant DMS-0100537
منابع مشابه
ar X iv : a st ro - p h / 02 04 26 5 v 1 1 6 A pr 2 00 2 A Large Area CCD Camera for the Schmidt Telescope at the Venezuelan National Astronomical Observatory
We have designed, constructed and put into operation a large area CCD camera that covers a large fraction of the image plane of the 1 meter Schmidt telescope at Llano del Hato in Venezuela. The camera consists of 16 CCD devices arranged in a 4 × 4 mosaic covering 2.3 × 3.5 of sky. The CCDs are 2048 × 2048 LORAL devices with 15μm pixels. The camera is optimized for drift scan photometry and obje...
متن کاملar X iv : 0 70 4 . 01 15 v 2 [ m at h . G T ] 9 A pr 2 00 7 Smooth maps with singularities of bounded K - codimensions ∗ † Yoshifumi ANDO
متن کامل
Learning Document Image Features With SqueezeNet Convolutional Neural Network
The classification of various document images is considered an important step towards building a modern digital library or office automation system. Convolutional Neural Network (CNN) classifiers trained with backpropagation are considered to be the current state of the art model for this task. However, there are two major drawbacks for these classifiers: the huge computational power demand for...
متن کاملar X iv : m at h / 06 04 63 5 v 1 [ m at h . A P ] 2 8 A pr 2 00 6 PARTIAL REGULARITY FOR HARMONIC MAPS , AND RELATED PROBLEMS
Via gauge theory, we give a new proof of partial regularity for harmonic maps in dimensions m ≥ 3 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of ”minimal” C regularity. The proof we present moreover extends to a large class of elliptic systems of quadratic growth.
متن کاملConnected Component Based Word Spotting on Persian Handwritten image documents
Word spotting is to make searchable unindexed image documents by locating word/words in a doc-ument image, given a query word. This problem is challenging, mainly due to the large numberof word classes with very small inter-class and substantial intra-class distances. In this paper, asegmentation-based word spotting method is presented for multi-writer Persian handwritten doc-...
متن کامل