#### Volume 17, issue 5 (2017)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
The surgery exact triangle in $\mathrm{Pin}(2)\mskip-1.5mu$–monopole Floer homology

### Francesco Lin

Algebraic & Geometric Topology 17 (2017) 2915–2960
##### Abstract

We prove the existence of an exact triangle for the $Pin\left(2\right)$–monopole Floer homology groups of three-manifolds related by specific Dehn surgeries on a given knot. Unlike the counterpart in usual monopole Floer homology, only two of the three maps are those induced by the corresponding elementary cobordism. We use this triangle to describe the Manolescu correction terms of the manifolds obtained by $\left(±1\right)$–surgery on alternating knots with Arf invariant $1$.

##### Keywords
Seiberg–Witten, monopoles, surgery, correction terms
Primary: 57M27