TY - JOUR
T1 - A signature invariant for stable maps of 3-manifolds into surfaces
AU - Saeki, Osamu
N1 - Funding Information:
Acknowledgements. The author has been supported in part by JSPS KAKENHI Grant Numbers JP15K13438, JP16K13754, JP16H03936, JP17H01090, JP17H06128.
Publisher Copyright:
© 2019 Editura Academiei Romane. All rights reserved.
PY - 2019
Y1 - 2019
N2 - Based on the signature formula for stable maps of closed oriented 4-manifolds into 3-manifolds, the author defined a Vassiliev type invariant of order one for stable maps of closed oriented 3-manifolds into surfaces. In this paper, we give an intrinsic formula for the invariant in terms of a certain linking form associated with a stable map for the 3-manifold. As a corollary, we get a signature formula for 4-manifolds with boundary in terms of their singular fibers of stable maps.
AB - Based on the signature formula for stable maps of closed oriented 4-manifolds into 3-manifolds, the author defined a Vassiliev type invariant of order one for stable maps of closed oriented 3-manifolds into surfaces. In this paper, we give an intrinsic formula for the invariant in terms of a certain linking form associated with a stable map for the 3-manifold. As a corollary, we get a signature formula for 4-manifolds with boundary in terms of their singular fibers of stable maps.
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M3 - Article
AN - SCOPUS:85088262283
VL - 64
SP - 541
EP - 563
JO - REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES
JF - REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES
SN - 0035-3965
IS - 4
ER -