If A is a unital associative algebra and u is invertible in A, one can define an algebra A, called the u-isotope of A, which is equal to A as a vector space but has a new product x ·u y = xuy. This isotope A (u) is again unital and associative but with a shifted identity element u. More generally there are definitions of isotope for several other classes of unital nonassociative algebras, notab...

The multi-variable Alexander polynomial (in the form of Conway’s potential function), when stripped of a redundant summand, is shown to be of the form ▽L(x1−x −1 1 , . . . , xm−x −1 m ) for some polynomial ▽L over Z; the Conway polynomial ∇L(z) coincides with z▽L(z, . . . , z). The coefficients of ▽L and of the power series ▽ L := ▽L/(▽K1 · · · ▽Km), where Ki denote the components of L, are fin...

Abstract Viterbo has conjectured that any Lagrangian in the unit co-disc bundle of a torus which is Hamiltonian isotopic to zero-section satisfies uniform bound on its spectral norm; recent result by Shelukhin showed this indeed case. The modest goal our note explore two natural generalisations geometric setting norm fails: first, passing Legendrian isotopies contactisation (recall isotopy can ...

If A is a unital associative algebra and u is invertible in A, one can define an algebra A, called the u-isotope of A, which is equal to A as a vector space but has a new product x ·u y = xuy. This isotope A (u) is again unital and associative but with a shifted identity element u. More generally there are definitions of isotope for several other classes of unital nonassociative algebras, notab...