Topological analogues of higher reciprocity laws

Postgraduate Thesis uoadl:1934046 629 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2017-09-22
Year:
2017
Author:
Cardaris Dimitris
Supervisors info:
Αριστείδης Κοντογεώργης, Καθηγητής, Μαθηματικών, ΕΚΠΑ
Σοφία Λαμπροπούλου, Καθηγήτρια, Μαθηματικών, ΕΜΠ
Ιωάννης Εμμανουήλ, Καθηγητής, ΕΚΠΑ
Original Title:
Τοπολογικά ανάλογα νόμων αντιστροφής
Languages:
Greek
Translated title:
Topological analogues of higher reciprocity laws
Summary:
Our aim is to describe topological analogues of higher reciprocity laws under the light of arithmetic topology. As a toy example we outline the case for quadratic reciprocity. CFT machinery helps us generalize this to n-th power reciprocity following Morishita. As expected, generalizing this to the non-commutative setting is more subtle. As a guiding principle we will use Gauss's point of view for the linking number. We sketch how this procedure arises naturally in the
formulation of modern physics following Kapranov and we draw parallels in-between those elds. In the end, we present a recent construction due to Minhyong of a Chern-Simons gauge theory for arithmetic itself and we discuss some potential directions for future progress in the non-abelian case.
Main subject category:
Science
Keywords:
Algebraic geomety, Number theory, Mathematical Physics, Low-dimensional topology
Index:
Yes
Number of index pages:
2
Contains images:
Yes
Number of references:
110
Number of pages:
127
File:
File access is restricted only to the intranet of UoA.

ptyxiakh.pdf
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