"September 2018. Volume 255. Number 1221 (fourth of 7 numbers)."
Includes bibliographical references
Introduction -- Basic setup -- The analysis of Morse-Bott singularities -- Floer homology for Morse-Bott singularities -- Pin(2)-monopole Floer homology
"In the present work we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped with a spin[superscript]c structure which is isomorphic to its conjugate, we define the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture."--Page v