arXiv subjects

Liviu I. Nicolaescu

Publications and source records attributed to Liviu I. Nicolaescu.

41 records · Page 3Linked to original sources

arXiv1998

On the Cappell-Lee-Miller glueing theorem

We formulate a more conceptual interpretation of the Cappell-Lee-Miller glueing/splitting theorem using the new language of asymptotic maps and asymptotic exactness. Additionally, we present an asymptotic description of the Mayer-Vietoris sequence naturally associated to the Cech cohomology of the sheaf of local solutions of a Dirac type operator. We discuss applications to eigenvalue estimates, approximation of obstruction bundles and glueing of determinant line bundles frequently arising in gauge theoretic problems. The operators involved in all these results need not be translation invariant.

math.DG↗

arXiv1998

Lattice points, Dedekind-Rademacher sums and a conjecture of Kronheimer and Mrowka

We express the number of lattice points inside certain simplices via Dedekind-Rademacher sums. As an application, we prove a conjecture of Kronheimer and Mrowka in the special case of Brieskorn spheres (with at most 4 singular fibers). This conjecture relates the Euler characteristic of the Seiberg-Witten-Floer homology to the Casson invariant.

math.DG↗

arXiv1997

Finite energy Seiberg-Witten moduli spaces on 4-manifolds bounding Seifert fibrations

We corrected a few errors in the previous submission. These do not affect any of the topological conclusions of the earlier version. We have also included a few observations about the Casson invariant of the Brieskorn homology spheres.

dg-ga↗

arXiv1997

Seiberg-Witten equations on tubes

We establish the adiabatic dissapearance of Seiberg-Witten tunnelings on tubes R x N, where N is an S^1 fibration over a Riemann surface.

dg-ga↗

arXiv1996

Adiabatic limits of Seiberg-Witten equations on Seifert manifolds

We present a simpler proof for the existence of adiabatic limits. Moreover, we added a new section where the adiabatic process is reversed and in some nondegenerate cases we deform the adiabatic limits to genuine irreducible solutions of the SW equations.

dg-ga↗