1995/01/01 by Peter J. Braam, Simon Donaldson · 5 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research
paper · doi:10.1007/978-3-0348-9217-9_10
openalex publication_date 1995/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
This paper is an exposition of Floer’s work which was completed circa 1989 and distributed in the shape of the two preprints [F1] (which is the preceding paper in this volume), [F2] (which was distributed as a «Preliminary version»). A description of the results was published in the Durham Proceedings [F3]. In this first part of the paper we deal with the «gauge theory» content of this work of Floer: that is, the proofs of the exact triangle in [F1] and the «excision axiom» of [F2]. This part is written with the aim of coming quickly to grips with the main geometrical points involved. The second part of our paper will take the topics further, introducing a more general framework for the results and describing the calculation scheme Floer developed in [F2]. The salient points here are in Sections II.1.3 where automorphisms of Floer homology are explained and in II.1.4, where Floer homology is computed for some important special manifolds. In section II.2.2 the exact triangle is discussed in a general setting, and in II.3.1, where it is explained how Kirby calculus gives rise to a set of exact sequences. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.