arXiv subjects
Publications and source records attributed to Razvan Gelca.
We show that the Kauffman bracket skein module of a cylinder over the torus embeds as a subalgebra of the noncommutative torus. Using this we derive nice formulas for the Jones-Wenzl idempotents and analyze the structure of the Kauffman bracket skein module of the unknot as a module over the Kauffman bracket skein module of a cylinder over the torus.
The results in the paper are related to the classification problem for invariant subspaces of multiplication operators in several variables. The main results consist of characterizations, in the two dimensional case, of ideals of polynomials and analytic functions which are closed in the relative topology induced by Bergman spaces on certain domains. This provides proofs of the Bergman space analogues of a conjecture of R. G. Douglas and V. Paulsen.
The paper gives a negative answer to the question whether one can perturb a Fredholm pair of index 0 by compact operators to a pair with exact Koszul complex.
The paper contains the proof, in dimension 2, of a conjecture of R. G. Douglas and V. Paulsen concerning the characterization of the ideals of polynomials which are closed in the relative topology induced by the Hardy space of the polydisk.
The paper contains examples of Fredholm n-tuples of operators that are of index 0 but cannot be perturbed by compact operators to n-tuples with exact Koszul complex.
The paper contains the construction of a topological quantum field theory in which gluings along surfaces with boundary are allowed. The construction is made by using quantum deformations of sl(2,C). In the construction there appears a sign obstruction to some of the Moore-Seiberg equations. This problem is solved by means of the Klein four group.
The paper contains the construction of a topological quantum field theory with corners that underlies the smooth topological quantum field theory of Lickorish. Among other things, a contraction formula for diagrams is proved, the presence of the skein relation at the level of manifolds with boundary is shown and an explanation for the surgery formula for invariants of closed manifolds is given.