OPEN PROBLEMS IN TOPOLOGY

ContentsxiiiProblems in Knot theoryby L. H. Kauffman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4870. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4891. Reidemeister Moves, Special Moves, Concordance . . . . . . . . . . 4892.KnottedStrings?.............................4923. Detecting Knottedness . . . . . . . . . . . . . . . . . . . . . . . . . 4944. Knots and Four Colors . . . . . . . . . . . . . . . . . . . . . . . . . 4975. The Potts Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4996. States, Crystals and the Fundamental Group . . . . . . . . . . . . . 5017. Vacuum-Vacuum Expectation and Quantum Group . . . . . . . . . 5068. Spin-Networks and Abstract Tensors . . . . . . . . . . . . . . . . . . 5099. Colors Again . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51010.Formations................................51411. Mirror-Mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518Problems in Infinite-Dimensional Topologyby J. E. West . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5231. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5252. CE: Cell-Like Images of ANR’s and Q-Manifolds . . . . . . . . . . . 5273. D: Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5324. SC: Shapes of Compacta . . . . . . . . . . . . . . . . . . . . . . . . 5365. ANR: Questions About Absolute Neighborhood Retracts . . . . . . 5426. QM: Topology of Q-manifolds . . . . . . . . . . . . . . . . . . . . . 5457. GA: Group Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5528. HS: Spaces of Automorphisms and Mappings . . . . . . . . . . . . . 5619.LS:LinearSpaces ............................56610. NLC: Non Locally Compact Manifolds . . . . . . . . . . . . . . . . 57011. TC: Topological Characterizations . . . . . . . . . . . . . . . . . . . 57312. N: Infinite Dimensional Spaces in Nature . . . . . . . . . . . . . . . 576References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581VII Topology Arising from Analysis 599Problems in C p -theoryby A. V. Arkhangel ′ skiĭ . . . . . . . . . . . . . . . . . . . . . . . . . . 601Problems in Topology Arising from Analysisby R. D. Mauldin .............................6171. Topologically Equivalent Measures on the Cantor Space . . . . . . . 6192. Two-Point Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6213. Pisot-Vijayaraghavan Numbers . . . . . . . . . . . . . . . . . . . . . 6224. Finite Shift Maximal Sequences Arising in Dynamical Systems . . . 623