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

Francesco Lin Massachusetts Institute of Technology, Cambridge, MA, USA
Available Formats:
Electronic ISBN: 978-1-4704-4819-6
Product Code: MEMO/255/1221.E
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $46.80 Click above image for expanded view A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture Francesco Lin Massachusetts Institute of Technology, Cambridge, MA, USA Available Formats:  Electronic ISBN: 978-1-4704-4819-6 Product Code: MEMO/255/1221.E  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$46.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 2552018; 162 pp
MSC: Primary 57;

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 ${\rm spin}^c$ 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.

• Chapters
• 1. Introduction
• 2. Basic setup
• 3. The analysis of Morse-Bott singularities
• 4. Floer homology for Morse-Bott singularities
• 5. $\mathrm {Pin}(2)$-monopole Floer homology

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Volume: 2552018; 162 pp
MSC: Primary 57;

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 ${\rm spin}^c$ 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.

• Chapters
• 1. Introduction
• 2. Basic setup
• 3. The analysis of Morse-Bott singularities
• 4. Floer homology for Morse-Bott singularities
• 5. $\mathrm {Pin}(2)$-monopole Floer homology
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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