Symplectic Rational Blow-Up and Embeddings of Rational Homology Balls

DSpace/Manakin Repository

Symplectic Rational Blow-Up and Embeddings of Rational Homology Balls

Citable link to this page

 

 
Title: Symplectic Rational Blow-Up and Embeddings of Rational Homology Balls
Author: Khodorovskiy, Tatyana
Citation: Khodorovskiy, Tatyana. 2012. Symplectic Rational Blow-Up and Embeddings of Rational Homology Balls. Doctoral dissertation, Harvard University.
Full Text & Related Files:
Abstract: We define the symplectic rational blow-up operation, for a family of rational homology balls \(B_n\), which appeared in Fintushel and Stern's rational blow-down construction. We do this by exhibiting a symplectic structure on a rational homology ball \(B_n\) as a standard symplectic neighborhood of a certain 2-dimensional Lagrangian cell complex. We also study the obstructions to symplectically rationally blowing up a symplectic 4-manifold, i.e. the obstructions to symplectically embedding the rational homology balls \(B_n\) into a symplectic 4-manifold. First, we present a couple of results which illustrate the relative ease with which these rational homology balls can be smoothly embedded into a smooth 4-manifold. Second, we prove a theorem and give additional examples which suggest that in order to symplectically embed the rational homology balls \(B_n\), for high \(n\), a symplectic 4-manifold must at least have a high enough \(c^2_1\) as well.
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:9572269
Downloads of this work:

Show full Dublin Core record

This item appears in the following Collection(s)

 
 

Search DASH


Advanced Search
 
 

Submitters