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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 16th 2012
• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeJan 17th 2012

Maybe you need some orientability assumption on the “space”.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJan 17th 2012
• (edited Jan 17th 2012)

Yes, the symbol $\int_X$ is fiber integration in the given cohomology theory $H$, and so we need $H$-orientation.

I have added a brief remark on this to the entry now. But this is by purpose still just under “Idea”. Eventually a more detailed discussion needs to be given.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJun 4th 2012

I had added some sentences to intersection pairing, mostly for the case in differential cohomology.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 31st 2014
• (edited May 31st 2014)

I gave intersection product an Idea-section and more references, only to realize that I had already an old entry intersection pairing. Have merged the material now. But of course it still needs more (more polishing, more content, etc.)