English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this article, we study a long exact sequence relating the mstanton homology of two homology 3-spheres which are obtained from each other by + 1 -surgery. We prove that the long exact sequence, via a short exact sequence of chain complex, is the same as the sequence defined by the exact triangle of cobordisms introduced by Floer. One development which has attracted a great deal of attention has been Floer's work on "instanton homology" of 3-manifolds [10], [14], [15], [19], [20], The basic idea is to find Floer homology groups HF*(Y) associated to an oriented 3-manifold Y by studying instantons on the tube Y X R. The theory applies in the first instance to homology 3-sphere Y. A fundamental question in Floer theory is the calculation of the Floer homology groups. A great step forward here was made by Floer who found an "exact triangle" of homomorphisms connecting the Floer homology groups of the 3-manifold Y with those of the 3-manifolds Y', Y" obtained from Y by Dehn surgery on a knot [6], [16], [17], [18]. This paper is based on the works of Floer, Braam and Donaldson. We consider a long exact sequence relating the instanton homology of two homology 3-spheres which are obtained from each other by ±1 -surgery. The third term is a Z^graded homology of the homology S X S which is associated to a knot in the homology 3~sphere via 0-surgery. We prove that the long exact sequence obtained via a short exact sequence of chain complex, is the same as the sequence defined by the exact triangle of cobordisms introduced by Floer in [16], [17]. Suppose that, as above, Y is an oriented homology 3-sphere and X^Y is a Communicated by K. Saito, October 16, 1995. 1991 Mathematics Subject Classification(s): 57N10, 55N35 *Department of Mathematics, National University of Singapore, Singapore 119260

The exactness theorem for Floer homology