Reading Seminar on Unstable Adams Spectral Sequence

This is a reading seminar on the Unstable Adams Spectral Sequence (UASS). The main topics are the construction of the UASS, λ-algebras, the EHP-sequence, and the applications to the proof of the Sullivan conjecture and a bit computation of the homotopy group of spheres.

The seminar meets on Tuesdays, 10:30 - 12:30 in the MPI seminar room.

Syllabus.

Contacts:

Nikolay Konovalov (nikolay [dot] konovalov [dot] p [at] gmail [dot] com) and Yuqing Shi (yuqing.shi [at] mpim-bonn [dot] mpg [dot] de).

Schedule:

Spring

1 April 30 Nikolai Overview

2 May 7 Yuqing The Bousfield–Kan homotopy spectral sequence of cosimplicial spaces

3 May 14 Emma Construction and convergence of the Fp-based unstable Adams spectral sequence

4 May 21 Liz E_2-page of the unstable Adams spectral sequence

5 May 28 Omer Proof of the Sullivan Conjecture: Part I

6 June 4 Vignesh Proof of the Sullivan Conjecture: Part II

7 June 18 Itamar The restricted lower central series spectral sequence

8 June 20 Yuqing Λ-algebras and the algebraic EHP sequence

9 June 25 Ningchuan The EHP-sequence

10 July 2 Lucas Nontriviality of the homotopy groups of the 4-dimensional sphere

Useful links:

H. Miller, The Sullivan Conjecture on Maps from Classifying Spaces.
A. K. Bousfield, D. M. Kan, Homotopy limits, completions and localizations.
A. K. Bousfield, D. M. Kan, The homotopy spectral sequence of a space with coefficients in a ring.
J. Lurie, Lecture notes on the Sullivan Conjecture.
E. Curtis, Some nonzero homotopy groups of spheres.
A. K. Bousfield, E. B. Curtis, D. M. Kan, D. G. Quillen, D. L. Rector, J. W. Schlesinger, The mod-p lower central series and the Adams spectral sequence.
A. K. Bousfield, E. Curtis, A spectral sequence for the homotopy of nice spaces.
R. Wellington, The Unstable Adams Spectral Sequence for Free Iterated Loop Spaces.
P. Goerss, Andre-Quillen cohomology and the homotopy groups of mapping space: understanding the E_2-term of the Boufield-Kan spectral sequence.
M. Bendersky, Unstable Towers in the Odd Primary Homotopy Groups of Spheres.
L. Schwartz, Unstable Modules over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture.
D. Quillen, Rational homotopy theory.
E. Curtis, Some relations between homotopy and homology.
D. Rector, An unstable Adams spectral sequence.
S. Ivanov, V. Romanovskii, A. Semenov, A Simple proof of Curtis' connectivity theorem for Lie powers.
E. Curtis, Lower central series of semi-simplicial complexes.
S. Devalapurkar, P. Haine, On the James and Hilton-Milnor Splittings, & the metastable EHP sequence.
J. Neisendorfer, Algebraic methods in unstable homotopy theory.

Spring
1	April 30	Nikolai	Overview
2	May 7	Yuqing	The Bousfield–Kan homotopy spectral sequence of cosimplicial spaces
3	May 14	Emma	Construction and convergence of the Fp-based unstable Adams spectral sequence
4	May 21	Liz	E_2-page of the unstable Adams spectral sequence
5	May 28	Omer	Proof of the Sullivan Conjecture: Part I
6	June 4	Vignesh	Proof of the Sullivan Conjecture: Part II
7	June 18	Itamar	The restricted lower central series spectral sequence
8	June 20	Yuqing	Λ-algebras and the algebraic EHP sequence
9	June 25	Ningchuan	The EHP-sequence
10	July 2	Lucas	Nontriviality of the homotopy groups of the 4-dimensional sphere