By Nikolai Proskurin

ISBN-10: 3540637516

ISBN-13: 9783540637516

The publication is an advent to the idea of cubic metaplectic types at the third-dimensional hyperbolic area and the author's learn on cubic metaplectic types on exact linear and symplectic teams of rank 2. the themes comprise: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein sequence, cubic theta capabilities, Whittaker features. a unique procedure is constructed and utilized to discover Fourier coefficients of the Eisenstein sequence and cubic theta services. The publication is meant for readers, with starting graduate-level historical past, attracted to extra learn within the concept of metaplectic varieties and in attainable applications.

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**Extra resources for Cubic Metaplectic Forms and Theta Functions**

**Example text**

A coloration could be called a state of the knot diagram in analogy to the energetic states of a physical system. In this case the system admits topological deformations, and in the case of three-coloring , we have seen that there is a way to preserve the state structure as the system is deformed . Invariant properties of states then become topological invariants of the knot or link. It is also possible to obtain topological invariants by considering all possible states (in some interpretation of that term- state) of a given diagram.

Eidemeister moves is called ambient isotopy. In fact, Reidemeister [REI] showed that two knots or links in three-dimensional space can be deformed continuously one into the other (the usual notion of ambient isotopy) if and only if any diagram (obtained by projection to a plane) of one link can be transformed into a diagram for the other link via a sequence of Reidemeister moves (: ,I,II,III). Thus these moves capture the full topological scenario for links in three-space. For a modern proof of Reidemeister's Theorem, see [BZ].

R )=w+landw (>4 )=w-1. Let a = -A3. 4 Letting A = t-1'4, we conclude that t-'5- tG = \'ft - f)G^W ^'! 1. Properties (1) and (ii) follow directly from the corresponding facts about GK• This completes the proof. // 51 One effect of this approach to the Jones polynomial is that we get an immediate and simple proof of the reversing property. 3. Let K and K' be two oriented links, so that K' is obtained by reversing the orientation of a component K1 C K. Let A = Zk(K1, K-K1) denote the total linking number of K1 with the remaining components of K.

### Cubic Metaplectic Forms and Theta Functions by Nikolai Proskurin

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