We consider Morse functions on compact manifolds possibly with boundary, and define their admissible cobordism group, based on generic maps into the plane that are submersions near the boundary. Then, we show that the cobordism group of Morse functions on surfaces with boundary is isomorphic to the cyclic group of order two. Our approach is based on the Stein factorizations: the novelty lies in the challenge that we consider Morse functions on manifolds with boundary and their cobordisms.
|Title of host publication||Contemporary Mathematics|
|Publisher||American Mathematical Society|
|Number of pages||19|
|Publication status||Published - 2016|
All Science Journal Classification (ASJC) codes