Some Representation stability results and generalizations

Some Representation stability results and generalizations

This thesis is about representation stability in the sense of Church and Farb. We show that sequences of cohomology groups of complements of arrangements of certain diagonal subspaces stabilize. We generalize the notion of representation stability to describe the behavior of products of stabilizing...

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Bibliographic Details
Main Author: Rapp, Artur
Contributors: Welker, Volkmar (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Language:English
Published: Philipps-Universität Marburg 2020
Subjects:
Topologie
Symmetrische Funktionen
Darstellungstheorie
symmetric functions
cohomology
Kohomologie
topology
representation theory
Mathematik
Mathematics
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Summary:This thesis is about representation stability in the sense of Church and Farb. We show that sequences of cohomology groups of complements of arrangements of certain diagonal subspaces stabilize. We generalize the notion of representation stability to describe the behavior of products of stabilizing sequences. Furthermore, we provide a representation theoretic formula for the cohomology of relative arrangements.
Physical Description:43 Pages
DOI:10.17192/z2020.0228

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