A monopole homology for integral homology 3-spheres

Weiping LI

Makale detayları

A monopole homology for integral homology 3-spheres

Yazarlar:

Weiping LI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2003 Vol.27 Issue 1, pp.125-160

Belge Tipi:

Makale

Yayın Tarihi:

12/2002

Belge Dili:

Türkçe

Document ID (Org No.):

2000748900

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

To an integral homology 3-sphere Y, we assign a well-defined  {\mathbb Z}-graded (monopole) homology MH*(Y, Ih(Q;  h0)) whose construction in principle follows from the instanton  Floer theory with the dependence of the spectral flow Ih(Q;  h0), where Q is the unique U(1)-reducible monopole of the  Seiberg-Witten equation on Y and h0 is a reference perturbation  datum.  The definition uses the moduli space of monopoles on Y \times  {\mathbb R} introduced by Seiberg-Witten in studying smooth  4-manifolds.  We show that the monopole homology MH*(Y,  Ih(Q; h0)) is invariant among Riemannian metrics with  same Ih(Q; h0).  This provides a chamber-like structure  for the monopole homology of integral homology 3-spheres.  The  assigned function MHSWF: \{Ih(Q; h0)\} \to \{MH*(Y,  Ih(Q; h0))\} is a topological invariant (as  Seiberg-Witten-Floer Theory).

 

To an integral homology 3-sphere Y, we assign a well-defined  {\mathbb Z}-graded (monopole) homology MH*(Y, Ih(Q;  h0)) whose construction in principle follows from the instanton  Floer theory with the dependence of the spectral flow Ih(Q;  h0), where Q is the unique U(1)-reducible monopole of the  Seiberg-Witten equation on Y and h0 is a reference perturbation  datum.  The definition uses the moduli space of monopoles on Y \times  {\mathbb R} introduced by Seiberg-Witten in studying smooth  4-manifolds.  We show that the monopole homology MH*(Y,  Ih(Q; h0)) is invariant among Riemannian metrics with  same Ih(Q; h0).  This provides a chamber-like structure  for the monopole homology of integral homology 3-spheres.  The  assigned function MHSWF: \{Ih(Q; h0)\} \to \{MH*(Y,  Ih(Q; h0))\} is a topological invariant (as  Seiberg-Witten-Floer Theory).

Makale detayları

A monopole homology for integral homology 3-spheres

Yazarlar:

Weiping LI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2003 Vol.27 Issue 1, pp.125-160

Belge Tipi:

Makale

Yayın Tarihi:

12/2002

Belge Dili:

Türkçe

Document ID (Org No.):

2000748900

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Turk. J. Math.

27

(2003)

125-160. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.27

iss.1.

Sayı

Makale detayları

A monopole homology for integral homology 3-spheres

Yazarlar: Weiping LI

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2003 Vol.27 Issue 1, pp.125-160

Belge Tipi: Makale

Yayın Tarihi: 12/2002

Belge Dili: Türkçe

Document ID (Org No.): 2000748900

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Turk. J. Math.

27

(2003)

125-160. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.27

iss.1.

Sayı

Yazarlar:

Weiping LI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2003 Vol.27 Issue 1, pp.125-160

Belge Tipi:

Makale

Yayın Tarihi:

12/2002

Belge Dili:

Türkçe

Document ID (Org No.):

2000748900

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098