Cohomology in algebra, geometry, physicsand statistics

An approach to the construction of virtual fundamental cycle/chain with integer coefficients

Around 2000, Kenji Fukaya and I proposed the construction of 
virtual fundamental cycle/chais with integer coeffients under the condition that 
the moduli spaces carry consistent  (relative) stable complex structures.  Starting with
the construction of virtual fundamental cycle/chains with rational coefficents, 
I will explain our ideas for the construction with integer coefficients.

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