ar X iv : m at h / 06 11 07 6 v 4 [ m at h . G T ] 1 4 Fe b 20 09 Virtual Homotopy

ar X iv : m at h / 06 07 79 4 v 2 [ m at h . G T ] 2 6 Fe b 20 07 MUTATION AND THE COLORED JONES POLYNOMIAL

We show examples of knots with the same polynomial invariants and hyperbolic volumes, with variously coinciding 2-cable polynomials and colored Jones polynomials, which are not mutants. AMS Classifications: 57M25, 57N70

ar X iv : m at h / 06 02 64 2 v 1 [ m at h . A G ] 2 8 Fe b 20 06 DIVISOR CLASSES AND THE VIRTUAL CANONICAL BUNDLE FOR GENUS 0 MAPS

Some divisor class relations for genus 0 curves are proved and used to compute the Cartier divisor class of the virtual canonical bundle for genus 0 maps to a smooth target. Many results here first appeared in [6] and [5]; our proofs use a completely different method.

ar X iv : 0 70 6 . 09 93 v 1 [ m at h . A T ] 7 J un 2 00 7 v 1 - PERIODIC HOMOTOPY GROUPS OF THE DWYER - WILKERSON SPACE

The Dwyer-Wilkerson space DI(4) is the only exotic 2-compact group. We compute its v1-periodic homotopy groups v 1 π∗(DI(4)).

ar X iv : m at h / 06 02 37 1 v 1 [ m at h . A G ] 1 7 Fe b 20 06 Braid Monodromy of Hypersurface Singularities

ar X iv : h ep - t h / 00 11 06 4 v 3 1 7 Fe b 20 04 Geometrization of the Quantum Effects

We present a conformally invariant generalized form of the free particle action by connecting the wave and particle aspects through gravity. Conformal invariance breaking is introduced by choosing a particular configuration of dynamical variables. This leads to the geometrization of the quantum aspects of matter.