TY - JOUR
T1 - SO(3) monopoles, level-one Seiberg-Witten moduli spaces, and Witten's conjecture in low degrees
AU - Feehan, Paul M.N.
AU - Leness, Thomas G.
N1 - Funding Information:
✩PMNF was supported in part by NSF grants DMS 9704174 and, through the Institute for Advanced Study, by DMS 9729992. TGL was supported in part by a Florida International University Provost’s Office Summer Research Grant. *Corresponding author. E-mail addresses: feehan@math.rutgers.edu, feehan@maths.tcd.ie (P.M.N. Feehan), lenesst@fiu.edu (T.G. Leness). URLs: http://www.math.rutgers.edu/~feehan (P.M.N. Feehan), http://www.fiu.edu/~lenesst (T.G. Leness). 1Current address: Department of Mathematics, Trinity College, University of Dublin, Dublin 2, Ireland.
PY - 2002/10/10
Y1 - 2002/10/10
N2 - We prove Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree c+2, with c=-1/4(7χ+11σ), for four-manifolds obeying some mild conditions, where χ and σ are their Euler characteristic and signature. We use the moduli space of SO(3) monopoles as a cobordism between a link of the Donaldson moduli space of anti-self-dual SO(3) connections and links of the moduli spaces of Seiberg-Witten monopoles. Gluing techniques allow us to compute contributions from Seiberg-Witten moduli spaces lying in the first (or 'one-bubble') level of the Uhlenbeck compactification of the moduli space of SO(3) monopoles.
AB - We prove Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree c+2, with c=-1/4(7χ+11σ), for four-manifolds obeying some mild conditions, where χ and σ are their Euler characteristic and signature. We use the moduli space of SO(3) monopoles as a cobordism between a link of the Donaldson moduli space of anti-self-dual SO(3) connections and links of the moduli spaces of Seiberg-Witten monopoles. Gluing techniques allow us to compute contributions from Seiberg-Witten moduli spaces lying in the first (or 'one-bubble') level of the Uhlenbeck compactification of the moduli space of SO(3) monopoles.
KW - Donaldson invariants
KW - SO(3) monopoles
KW - Seiberg-Witten invariants
KW - Smooth four manifolds
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U2 - 10.1016/S0166-8641(01)00233-4
DO - 10.1016/S0166-8641(01)00233-4
M3 - Article
AN - SCOPUS:0038690263
SN - 0166-8641
VL - 124
SP - 221
EP - 326
JO - Topology and its Applications
JF - Topology and its Applications
IS - 2
ER -