# A computation of the ring structure in wrapped Floer homology

## TL;DR

This paper explicitly computes the ring structure in wrapped Floer homology for certain real Lagrangians in $A_k$-type Milnor fibers, utilizing Seidel representation and Viterbo transfer to handle technical complexities.

## Contribution

It provides the first explicit calculation of the ring structure in wrapped Floer homology for specific Lagrangians in Milnor fibers, advancing understanding of symplectic topology.

## Key findings

- Explicit ring structure computations for real Lagrangians in $A_k$-type Milnor fibers.
- Application of Seidel representation in wrapped Floer homology.
- Use of Viterbo transfer to relate v-shaped and standard wrapped Floer homology.

## Abstract

We give an explicit computation of the ring structure in wrapped Floer homology of a class of real Lagrangians in $A_k$-type Milnor fibers. In the $A_k$-type plumbing description, those Lagrangians correspond to the cotangent fibers or the diagonal Lagrangians. The main ingredient of the computation is to apply a version of the Seidel representation. For a technical reason, we first carry out computations in v-shaped wrapped Floer homology, and this in turn gives the desired ring structure via the Viterbo transfer map.