Top Global Course Special Lectures 1 “Loop space decompositions in homotopy theory with applications to Poincaré Duality spaces”
“Loop space decompositions in homotopy theory with applications to Poincaré Duality spaces” Lecture 5 Prof. Stephen Theriault (University of Southampton)
A great challenge in homotopy theory is determining properties of the homotopy groups of finite simplyconnected CWcomplexes. One approach is to try to decompose the based loops on such a space into a product of more recognizable factors. In these talks we will investigate a new loop space decomposition method that applies to many interesting families of spaces, with special focus on various classes of Poincaré Duality complexes. Among the consequences are resolutions of instances of famous conjectures: by Moore on the relation between the torsion and rational homotopy groups, and by Gromov and ViguéPoirrier on exponential growth in the rational homology of free loop spaces.
You can download lecture materials(board writings) of 1st – 5th lectures from Resources(10).

 “Loop space decompositions in homotopy theory with applications to Poincaré Duality spaces” Lecture 4

Prof. Stephen Theriault (University of Southampton)
Oct. 14, 2021 1:45:45 English

 “Loop space decompositions in homotopy theory with applications to Poincaré Duality spaces” Lecture 5

Prof. Stephen Theriault (University of Southampton)
Oct. 15, 2021 1:38:43 English

 Loop space decompositions in homotopy theory with applications to Poincaré Duality spaces

 Loop space decompositions

 A decomposition method

 Example: Poincaré Duality complex

 Recall an ndimensional PD complex

 Inert maps are connected sums

 Reminder

 The Homology of Loops on PDcomplexes

 Exponential Growth in the rational homology of free loop space

 Additional Results are open Problems
Details
 Year/Term
 2021
 Date
 October 7th to October 15th, 2021
 Faculty/
Graduate School  Graduate School of Science
 Instructor name
 Stephen Theriault（University of Southampton）
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