Thomas H. Parker

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We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of [IP4]. The main step is the construction of a compact space of ‘V -stable’ maps. Simple special cases include the Hurwitz numbers for algebraic curves and the(More)
In the symplectic category there is a ‘connect sum’ operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a symplectic sum Z = X#Y in terms of the relative GW invariants ofX and Y . Several applications to enumerative geometry are(More)
Let Σ be a compact Riemann surface. Any sequence fn : Σ —> M of harmonic maps with bounded energy has a "bubble tree limit" consisting of a harmonic map /o : Σ -> M and a tree of bubbles fk : S 2 -> M. We give a precise construction of this bubble tree and show that the limit preserves energy and homotopy class, and that the images of the fn converge(More)
This paper develops the Riemannian geometry of classical gauge theories Yang-Mills fields coupled with scalar and spinor fields on compact four-dimensional manifolds. Some important properties of these fields are derived from elliptic theory : regularity, an "energy gap theorem", the manifold structure of the configuration space, and a bound for the(More)
In myeloma, the prognostic impact of different strategies used to detect chromosome 13 deletion (Delta13) remains controversial. To address this, we compared conventional cytogenetics and interphase fluorescence in situ hybridization (iFISH) in a large multicenter study (n=794). The ability to obtain abnormal metaphases was associated with a poor prognosis,(More)
We prove a structure theorem for the Gromov-Witten invariants of compact Kähler surfaces with geometric genus pg > 0. Under the technical assumption that there is a canonical divisor that is a disjoint union of smooth components, the theorem shows that the GW invariants are universal functions determined by the genus of this canonical divisor components and(More)
INTRODUCTION Despite effective in vitro preclinical strategies to identify cardiovascular (CV) liabilities, there remains a need for early functional assessment prior to complex in vivo mammalian models. The larval zebrafish (Danio rerio, Zf) has been suggested for this role: previous data suggest that cardiac electrophysiology and vascular ultrastructure(More)
In a series of 41 pancreatoduodenectomies the Whipple procedure was done in 27 patients and total pancreatoduodenectomy in 14 others with two postoperative deaths. Among 39 survivors, seven developed evidence of stomal ulcer 20 days to six years after operation; details of their courses are summarized. Proven stomal ulcer occurred in five of 14 patients who(More)
C. Taubes has recently defined Gromov invariants for symplectic four-manifolds and related them to the Seiberg-Witten invariants ([T1], [T2]). Independently, Y. Ruan and G. Tian defined symplectic invariants based on ideas of Witten ([RT]). While similar in spirit, these two sets of invariants are quite different in their details. In this note we show that(More)