The geometry of continued fractions and the topology of surface singularities

@misc{citeulike:234892, abstract = {We survey the use of continued fraction expansions in the algebraical and topological study of complex analytic singularities. We also prove new results, firstly concerning a geometric duality with respect to a lattice between plane supplementary cones and secondly concerning the existence of a canonical plumbing structure on the abstract boundaries (also called links) of normal surface singularities. The duality between supplementary cones gives in particular a geometric interpretation of a duality discovered by Hirzebruch between the continued fraction expansions of two numbers l \>1 and l/(l - 1).}, author = {Popescu-Pampu, Patrick }, citeulike-article-id = {234892}, eprint = {math.GT/0506432}, keywords = {continued, fractions, geometry, topology}, month = {June}, posted-at = {2005-11-25 10:02:20}, priority = {2}, title = {The geometry of continued fractions and the topology of surface singularities}, url = {http://arxiv.org/abs/math.GT/0506432}, year = {2005} }

TY - ELEC ID - citeulike:234892 L3 - citeulike-article-id:234892 TI - The geometry of continued fractions and the topology of surface singularities N2 - We survey the use of continued fraction expansions in the algebraical and topological study of complex analytic singularities. We also prove new results, firstly concerning a geometric duality with respect to a lattice between plane supplementary cones and secondly concerning the existence of a canonical plumbing structure on the abstract boundaries (also called links) of normal surface singularities. The duality between supplementary cones gives in particular a geometric interpretation of a duality discovered by Hirzebruch between the continued fraction expansions of two numbers l >1 and l/(l - 1). KW - continued KW - fractions KW - geometry KW - topology AU - Popescu-Pampu, Patrick PY - 2005/06/21/ UR - http://arxiv.org/abs/math.GT/0506432 ER -