Oberwolfach Surgery Seminar 2012: General information
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#[[Oberwolfach Surgery Seminar 2012: Program#Spivak normal fibration|Spivak normal fibration]] [[User:Diarmuid Crowley|DC]] | #[[Oberwolfach Surgery Seminar 2012: Program#Spivak normal fibration|Spivak normal fibration]] [[User:Diarmuid Crowley|DC]] | ||
#[[Oberwolfach Surgery Seminar 2012: Program#Normal invariants and surgery below the middle dimension|Normal invariants and surgery below the middle dimension]] [[User:Diarmuid Crowley|DC]] | #[[Oberwolfach Surgery Seminar 2012: Program#Normal invariants and surgery below the middle dimension|Normal invariants and surgery below the middle dimension]] [[User:Diarmuid Crowley|DC]] | ||
− | #[[Oberwolfach Surgery Seminar 2012: Program#L-groups of rings with involution| | + | #[[Oberwolfach Surgery Seminar 2012: Program#L-groups of rings with involution|Immersions, the Wall form and formations]] [[User:Diarmuid Crowley|DC]] |
− | #[[Oberwolfach Surgery Seminar 2012: Program#Surgery obstructions| | + | #[[Oberwolfach Surgery Seminar 2012: Program#Surgery obstructions|L-groups and Wall realisation]] [[User:Diarmuid Crowley|DC]] |
#[[Oberwolfach Surgery Seminar 2012: Program#The geometric surgery exact sequence|The geometric surgery exact sequence]] [[User:Diarmuid Crowley|DC]] | #[[Oberwolfach Surgery Seminar 2012: Program#The geometric surgery exact sequence|The geometric surgery exact sequence]] [[User:Diarmuid Crowley|DC]] | ||
#[[Oberwolfach Surgery Seminar 2012: Program#The TOP surgery exact sequence|The TOP surgery exact sequence]] [[User:Tibor Macko|TM]] | #[[Oberwolfach Surgery Seminar 2012: Program#The TOP surgery exact sequence|The TOP surgery exact sequence]] [[User:Tibor Macko|TM]] | ||
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=== Algebraic surgery === | === Algebraic surgery === | ||
#[[Oberwolfach Surgery Seminar 2012: Program#Structured chain complexes|Structured chain complexes]] [[User:Ranicki|AR]] | #[[Oberwolfach Surgery Seminar 2012: Program#Structured chain complexes|Structured chain complexes]] [[User:Ranicki|AR]] |
Revision as of 19:44, 27 May 2012
Contents |
1 Prerequisites
The prerequisites for the seminar are a solid knowledge of the basics of differential and algebraic topology, meaning: manifolds, Poincaré duality, bundles, cobordism, transversality, generalized homology and cohomology, homotopy groups.
Participants should be familiar with the ideas covered in the first 7 chapters of the book [Ranicki2002]. However material from sections 2.2., 4.2, 5.4, 7.3 will be covered during the seminar. In addition participants should be familiar with the basics of spectra in stable homotopy theory. A good reference here is [Hatcher2002, Section 4.F].
The main references for the material covered in the seminar are [Ranicki1979], [Ranicki1992], [Kühl&Macko&Mole2011] and [Wall1999].
2 Schedule
2.1 Geometric surgery
- Bundle theories DC
- Spivak normal fibration DC
- Normal invariants and surgery below the middle dimension DC
- Immersions, the Wall form and formations DC
- L-groups and Wall realisation DC
- The geometric surgery exact sequence DC
- The TOP surgery exact sequence TM
2.2 Algebraic surgery
- Structured chain complexes AR
- Symmetric and quadratic signature AR
- Algebraic surgery and L-groups via chain complexes AR
- Examples of Poincaré complexes Speakers TBA
- Additive categories with chain duality and categories over complexes TM
- Generalized homology theories TM
- The normal complexes TM
2.3 Algebraic surgery versus geometric surgery
- The algebraic surgery exact sequence AR
- The topological block bundle obstruction TM
- The surgery obstruction TM
- The geometric and algebraic surgery exact sequences AR
- Examples and related developments AR