5,440 research outputs found
Delocalized Chern character for stringy orbifold K-theory
In this paper, we define a stringy product on K^*_{orb}(\XX) \otimes \C ,
the orbifold K-theory of any almost complex presentable orbifold \XX. We
establish that under this stringy product, the de-locaized Chern character
ch_{deloc} : K^*_{orb}(\XX) \otimes \C \longrightarrow H^*_{CR}(\XX), after a
canonical modification, is a ring isomorphism. Here H^*_{CR}(\XX) is the
Chen-Ruan cohomology of \XX. The proof relies on an intrinsic description of
the obstruction bundles in the construction of Chen-Ruan product. As an
application, we investigate this stringy product on the equivariant K-theory
of a finite group with the conjugation action. It turns out that
the stringy product is different from the Pontryajin product (the latter is
also called the fusion product in string theory).Comment: 34 pages. Final version to appear in Trans. of AMS. Improve the
expositions and Change of the title thanks the referee
Exact triangles in monopole homology and the Casson-Walker invariant
We establish the exact triangle in Seiberg-Witten-Floer theory relating the
monopoloe homologies of any two closed 3-manifolds which are obtained from each
other by -surgery. We also show that the sum of the modified version of
the Seiberg-Witten invariants for any closed rational homology 3-sphere
over all structures equals to
where is the Casson-Walker invariant.Comment: 35 pages, 3 figure
Equivariant Seiberg-Witten Floer Homology
This paper circulated previously in a draft version. Now, upon general
request, it is about time to distribute the more detailed (and much longer)
version. The main technical issues revolve around the fine structure of the
compactification of the moduli spaces of flow lines and the obstruction bundle
technique, with related gluing theorems, needed in the proof of the topological
invariance of the equivariant version of the Floer homology.Comment: 162 pages, LaTex, 1 figure, diagrams (xypic
Exact triangles in Seiberg-Witten Floer theory. Part IV: Z-graded monopole homology
Some aspects of the construction of SW Floer homology for manifolds with
non-trivial rational homology are analyzed. In particular, the case of
manifolds that are obtained as zero-surgery on a knot in a homology sphere, and
for torsion spinc structures. We discuss relative invariants in the case of
torsion spinc structures.Comment: 34 page
Exact triangles in Seiberg-Witten Floer theory. Part III: proof of exactness
This is the third part of the work on the exact triangles. We construct chain
homomorphisms and show exactness of the resulting sequence.Comment: 69 pages, 4 figure
Exact triangles in Seiberg-Witten Floer theory. Part II: geometric limits of flow lines
This is the second part of the proof of the exact traiangles in
Seiberg-Witten Floer theory. We analyse the splitting and gluing of flow lines
of the Chern-Simons-Dirac functional when the underlying three-manifold splits
along a torus. (two corrections added)Comment: 71 pages, 3 figure
- …