@article{b337a6a130504f0d9efd3cda9a430987,
title = "The surgery exact triangle in Pin(2)–onopole Floer homology",
abstract = "We prove the existence of an exact triangle for the Pin.(2)–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 (±1)–surgery on alternating knots with Arf invariant 1.",
author = "Francesco Lin",
note = "Funding Information: Acknowledgements The author would like to thank his advisor Tom Mrowka for the support throughout the development of this project, Tye Lidman and Ciprian Manolescu for the useful comments, and the referee for carefully reading the manuscript and suggesting many improvements. Part of the work was carried over while the author was visiting the University of Pisa. He would like to express his gratitude to them, and in particular Bruno Martelli, for their hospitality. This work was partially supported by NSF grants DMS-0805841 and DMS-1005288. Publisher Copyright: {\textcopyright} 2017, Mathematical Sciences Publishers. All rights reserved.",
year = "2017",
month = sep,
day = "19",
doi = "10.2140/agt.2017.17.2915",
language = "English (US)",
volume = "17",
pages = "2915--2960",
journal = "Algebraic and Geometric Topology",
issn = "1472-2747",
publisher = "Agriculture.gr",
number = "5",
}