Abstract
Floer constructed instanton homology for integral homology three-spheres. In this paper, we extend instanton Floer homology to lens spaces L(p, q). Moreover we show a gluing formula for a variant of Donaldson invariant along lens spaces. As an application, we prove that X= ℂℙ2#ℂℙ2 does not admit a decomposition X=X1∪X2. Here X1 and X2 are oriented, simply connected, non-spin four-manifolds with b+ = 1 and with boundary L(p, 2), and p is a prime number of the form 16N + 1.
Original language | English |
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Pages (from-to) | 237-281 |
Number of pages | 45 |
Journal | Mathematische Zeitschrift |
Volume | 273 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - Jan 1 2013 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
Instanton Floer homology for lens spaces. / Sasahira, Hirofumi.
In: Mathematische Zeitschrift, Vol. 273, No. 1-2, 01.01.2013, p. 237-281.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Instanton Floer homology for lens spaces
AU - Sasahira, Hirofumi
PY - 2013/1/1
Y1 - 2013/1/1
N2 - Floer constructed instanton homology for integral homology three-spheres. In this paper, we extend instanton Floer homology to lens spaces L(p, q). Moreover we show a gluing formula for a variant of Donaldson invariant along lens spaces. As an application, we prove that X= ℂℙ2#ℂℙ2 does not admit a decomposition X=X1∪X2. Here X1 and X2 are oriented, simply connected, non-spin four-manifolds with b+ = 1 and with boundary L(p, 2), and p is a prime number of the form 16N + 1.
AB - Floer constructed instanton homology for integral homology three-spheres. In this paper, we extend instanton Floer homology to lens spaces L(p, q). Moreover we show a gluing formula for a variant of Donaldson invariant along lens spaces. As an application, we prove that X= ℂℙ2#ℂℙ2 does not admit a decomposition X=X1∪X2. Here X1 and X2 are oriented, simply connected, non-spin four-manifolds with b+ = 1 and with boundary L(p, 2), and p is a prime number of the form 16N + 1.
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UR - http://www.scopus.com/inward/citedby.url?scp=84872284446&partnerID=8YFLogxK
U2 - 10.1007/s00209-012-1003-2
DO - 10.1007/s00209-012-1003-2
M3 - Article
AN - SCOPUS:84872284446
VL - 273
SP - 237
EP - 281
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 1-2
ER -