ar X iv : m at h - ph / 0 60 80 01 v 1 3 1 Ju l 2 00 6 1 Modular Invariants and Fischer - Griess Monster 1

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : m at h - ph / 0 20 80 10 v 1 6 A ug 2 00 2 ALGEBRAIC INVARIANTS , DETERMINANTS , AND CAYLEY – HAMILTON THEOREM FOR HYPERMATRICES . THE FOURTH – RANK CASE

We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley–Hamilton theorem for hypermatrices.

ar X iv : m at h / 03 07 23 0 v 1 [ m at h . A G ] 1 6 Ju l 2 00 3 EXPLICIT EQUATIONS OF SOME ELLIPTIC MODULAR SURFACES

We present explicit equations of semi-stable elliptic surfaces (i.e., having only type In singular fibers) which are associated to the torsion-free genus zero congruence subgroups of the modular group as classified by A. Sebbar.

ar X iv : m at h / 06 07 79 4 v 1 [ m at h . G T ] 3 1 Ju l 2 00 6 MUTATION AND THE COLORED JONES POLYNOMIAL

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

ar X iv : 0 80 7 . 00 58 v 2 [ m at h . D G ] 1 6 Ju l 2 00 8 EQUIVARIANT DIFFERENTIAL CHARACTERS AND SYMPLECTIC REDUCTION

We describe equivariant differential characters (classifying equi-variant circle bundles with connections), their prequantization, and reduction.