Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Spin Borromean surgeries

Author: Gwénaël Massuyeau
Journal: Trans. Amer. Math. Soc. 355 (2003), 3991-4017
MSC (2000): Primary 57M27; Secondary 57R15
Published electronically: June 24, 2003
MathSciNet review: 1990572
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In 1986, Matveev defined the notion of Borromean surgery for closed oriented $3$-manifolds and showed that the equivalence relation generated by this move is characterized by the pair (first Betti number, linking form up to isomorphism).

We explain how this extends for $3$-manifolds with spin structure if we replace the linking form by the quadratic form defined by the spin structure. We then show that the equivalence relation among closed spin $3$-manifolds generated by spin Borromean surgeries is characterized by the triple (first Betti number, linking form up to isomorphism, Rochlin invariant modulo  $8$).

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57M27, 57R15

Retrieve articles in all journals with MSC (2000): 57M27, 57R15

Additional Information

Gwénaël Massuyeau
Affiliation: Laboratoire Jean Leray, UMR 6629 CNRS/Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France

PII: S 0002-9947(03)03071-X
Keywords: 3-manifolds, finite type invariants, spin structures, $Y$-graphs
Received by editor(s): April 16, 2001
Received by editor(s) in revised form: April 2, 2002
Published electronically: June 24, 2003
Additional Notes: Commutative diagrams were drawn with Paul Taylor’s package
Article copyright: © Copyright 2003 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia