A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture

ISBN-13: 9781470429638 / Angielski

Francesco Lin

Opis

In the present work the author generalizes 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 equipped with a ${ m spin}^c$ structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.

Spis treści

• Introduction
• Basic setup
• The analysis of Morse-Bott singularities
• Floer homology for Morse-Bott singularities
• Pin(2)-monopole Floer homology
• Bibliography