Do you want to publish a course? Click here

Seiberg-Witten-Floer Theory for Homology 3-Spheres

61   0   0.0 ( 0 )
 Added by Bryan Wang
 Publication date 1996
  fields
and research's language is English
 Authors Bai-Ling Wang




Ask ChatGPT about the research

We give the definition of the Seiberg-Witten-Floer homology group for a homology 3-sphere. Its Euler characteristic number is a Casson-type invariant. For a four-manifold with boundary a homology sphere, a relative Seiberg-Witten invariant is defined taking values in the Seiberg-Witten-Floer homology group, these relative Seiberg-Witten invariants are applied to certain homology spheres bounding Stein surfaces.



rate research

Read More

We construct a generalization of the Seiberg-Witten Floer spectrum for suitable three-manifolds $Y$ with $b_1(Y)>0$. For a cobordism between three-manifolds we define Bauer-Furuta maps on these new spectra, and additionally compute some examples.
157 - Eaman Eftekhary 2013
We show that if a prime homology sphere has the same Floer homology as the standard three-sphere, it does not contain any incompressible tori.
We derive a family of matrix models which encode solutions to the Seiberg-Witten theory in 4 and 5 dimensions. Partition functions of these matrix models are equal to the corresponding Nekrasov partition functions, and their spectral curves are the Seiberg-Witten curves of the corresponding theories. In consequence of the geometric engineering, the 5-dimensional case provides a novel matrix model formulation of the topological string theory on a wide class of non-compact toric Calabi-Yau manifolds. This approach also unifies and generalizes other matrix models, such as the Eguchi-Yang matrix model, matrix models for bundles over $P^1$, and Chern-Simons matrix models for lens spaces, which arise as various limits of our general result.
330 - Jianfeng Lin , Daniel Ruberman , 2017
We study the Seiberg-Witten invariant $lambda_{rm{SW}} (X)$ of smooth spin $4$-manifolds $X$ with integral homology of $S^1times S^3$ defined by Mrowka, Ruberman, and Saveliev as a signed count of irreducible monopoles amended by an index-theoretic correction term. We prove a splitting formula for this invariant in terms of the Fr{o}yshov invariant $h(X)$ and a certain Lefschetz number in the reduced monopole Floer homology of Kronheimer and Mrowka. We apply this formula to obstruct existence of metrics of positive scalar curvature on certain 4-manifolds, and to exhibit new classes of integral homology $3$-spheres of Rohlin invariant one which have infinite order in the homology cobordism group.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا