An alternative definition of cobordism map of ECH

Abstract

In this article, we reformulate the cobordism map of embedded contact homology, which is induced by exact symplectic cobordism and defined as direct limit of homomorphisms called filtered ECH cobordism map. The filtered ECH cobordism map is defined by counting embedded holomorphic curves with zero ECH index and we prove that it is independent on almost complex structure by Seiberg Witten theory. Moreover, our definition in fact is equivalent to the existing definition.