During the Fall term 2019 we will work on Manolescu's paper "Lectures on the Triangulation conjecture"

Meeting:

We will meet on Fridays 11am - 12pm in RLM 8.136

References:

We will follow these references:

• [M] C. Manolescu - Lectures on the Triangulation conjecture
• [DHST] I. Dai, J. Hom, M. Stoffregen, L. Truong - An Infinite-Rank Summand of the Homology Cobordism Group
• [M03] C. Manolescu - Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0
• [M16] C. Manolescu - The Conley Index, Gauge Theory and Triangulations

Notes:

Here you can find some notes on the seminar, courtesy of Jackson Van Dyke

Here you can find the notes of my talk about the Conley Index

Provisional Schedule:

August 30 - Arun

Organisational meeting

September 13 - Charlie

Overview and background material:

[M], [DHST]

September 20 Will

Reduction of the problem to an homology cobordism one

September 27 Leon

Seiberg-Witten equations, finite dimensional approximation

October 4 Riccardo

Finite dimensional approximation (cont.) and Conley Index

[M], [M03], [M16]

October 11 Ricky

Pin_2- equivariance of SWF homotopy type

October 18 Jackson

Definition of the homology cobordism invariants

October 25 Arun

Equivariant Spanier-Whitehead duality

November 1

CANCELLED

November 8 Jonathan

Involutive HF homology Part 1

November 15 Kai

Involutive HF homology Part 2

November 22 Leon

Proof of the main theorem