A Morse-Bott approach to monopole Floer homology and the triangulation conjecture / Francesco Lin.

Format:

Book

Author/Creator:

Lin, Francesco, 1988- author.

Series:

Memoirs of the American Mathematical Society ; Volume 255, Number 1221.

Memoirs of the American Mathematical Society ; Volume 255, Number 1221

Language:

English

Subjects (All):

Triangulation.

Physical Description:

1 online resource (174 pages).

Edition:

1st ed.

Other Title:

Morse Bott approach to monopole Floer homology and the triangulation conjecture

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

Summary:

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.

Contents:

Cover

Title page

Chapter 1. Introduction

Chapter 2. Basic setup

2.1. The monopole equations

2.2. Blowing up the configuration spaces

2.3. Completion and slices

2.4. Perturbations

Chapter 3. The analysis of Morse-Bott singularities

3.1. Hessians and Morse-Bott singularities

3.2. Moduli spaces of trajectories

3.3. Transversality

3.4. Compactness and finiteness

3.5. Gluing

3.6. The moduli space on a cobordism

Chapter 4. Floer homology for Morse-Bott singularities

4.1. Homology of smooth manifolds via stratified spaces

4.2. Floer homology

4.3. Invariance and functoriality

Chapter 5. \Pin-monopole Floer homology

5.1. An involution in the theory

5.2. Equivariant perturbations and Morse-Bott transversality

5.3. Invariant chains and Floer homology

5.4. Some computations

5.5. Manolescu's invariant and the Triangulation conjecture

Bibliography

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-4819-X

OCLC:

1042567976