  The cross-blockchain transaction (CBT) serves as a cornerstone for the
next-generation, blockchain-based data management systems. However,
state-of-the-art CBT models do not address the effect of the possible local
fork suspension that might invalidate the entire CBT. This paper takes an
algebraic-topological approach to abstract the blockchains and their
transactions into simplicial complexes and shows that CBTs cannot complete in
either a \textit{committed} or an \textit{aborted} status by a $t$-resilient
message-passing protocol. This result implies that a more sophisticated model
is in need to support CBTs and, thus, sheds light on the future blockchain
designs.
