4,219 research outputs found
Integral bases for TQFT modules and unimodular representations of mapping class groups
We construct integral bases for the SO(3)-TQFT-modules of surfaces in genus
one and two at roots of unity of prime order and show that the corresponding
mapping class group representations preserve a unimodular Hermitian form over a
ring of algebraic integers. For higher genus surfaces the Hermitian form
sometimes must be non-unimodular. In one such case, genus 3 and p=5, we still
give an explicit basis
Some remarks on orbit sets of unimodular rows
We give a cohomological interpretation of orbit sets of unimodular rows of
length d+1 over smooth algebras of Krull dimension d.Comment: 18 page
Rationally Isomorphic Hermitian Forms and Torsors of Some Non-Reductive Groups
Let be a semilocal Dedekind domain. Under certain assumptions, we show
that two (not necessarily unimodular) hermitian forms over an -algebra with
involution, which are rationally ismorphic and have isomorphic semisimple
coradicals, are in fact isomorphic. The same result is also obtained for
quadratic forms equipped with an action of a finite group. The results have
cohomological restatements that resemble the Grothendieck--Serre conjecture,
except the group schemes involved are not reductive. We show that these group
schemes are closely related to group schemes arising in Bruhat--Tits theory.Comment: 27 pages. Changes from previous version: Section 5 was split into two
sections, several proofs have been simplified, other mild modification
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