•
Exotic smooth structures on topological fibre bundles A. (with Sebastian Goette)
| |
Revised version
January 28, 2012
|
|
| |
We use a variation of Hatcher's construction to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension and and show that the relative higher Reidemeister torsion is the Poincare dual of the image of the relative smooth structure class (constructed in Part B) in the homology of the base.
|
|
•
Exotic smooth structures on topological fibre bundles B. (with Sebastian Goette and Bruce Williams)
| |
Revised version
January 26, 2012
|
|
| |
This paper used to be the appendix of the Exotic smooth structures paper. It is now a separate paper at the suggestion of the referee. Given a smooth bundle, an exotic smooth structure is a smooth structure different from the one already given. Such structures are classified, rationally and stably, by a homology class in the total space of the bundle. We call it the relative smooth structure class.
|
|
•
Continuous cluster categories II: Continuous cluster-tilted categories. (with Gordana Todorov)
| |
Revised version
July 16, 2011
|
|
| |
This is the third paper in a series. (We are writing a ``prequel: Continuous Frobenius catagories'' (CF) giving an easy way to see the triangulated structure of the continuous cluster categories in CCC I.) This paper starts with a review of the definitions and results of CCC I. This revised version has complete proofs of the main theorems, namely (1) the rational and continuous cluster-tilted categories are abelian and (2) they are isomorphic to categories of string modules over the Jacobian algebra of an infinite quiver with potential. We will post CF on the arXiv first.
|
|
•
A proof of the strong no loop conjecture. (with Shiping Liu and Charles Paquette)
| |
ArXiv:1103.5361
Advances in Mathematics 228 (2011) 2731-2742.
|
|
| |
In terms of a quiver with relations, the strong no loop conjecture states that, if the quiver has a loop at a vertex, the simple module at the vertex has infinite projective dimension.
|
|
•
Exceptional sequences, braid groups and clusters,
Groups, Algebras and Applications
| |
(Proceedings of XVIII LATIN-AMERICAN ALGEBRA COLLOQUIUM Sao Pedro, August 7, 2009, Cesar P. Milies, Ed.) Contemporary Mathematics (2011) 537, 227-240.
|
|
|
•
Exceptional sequences and clusters.
(with Ralf Schiffler)
|
|
•
Iterated integrals of superconnections.
|
•
Twisting cochains and higher torsion.
| |
arXiv:0212383v3
July 3, 2011.
To appear in Journal of Homotopy and Related Structures.
|
|
|
|
•
Families of regular matroids.
|
|
•
Cluster Complexes via Semi-Invariants.
(with Kent Orr, Gordana Todorov, Jerzy Weyman)
|
|
|
•
Stability theorem for smooth pseudoisotopies
|
|
•
The generalized Grassmann invariant
(This is my original paper about pictures.)
|
|
•
Postnikov Invariants and Pseudoisotopy
|
igusa@brandeis.edu