《代數配邊理論(英文版)》是一部很難得的介紹代數配邊理論的專著,內容精煉簡短!洞鷶蹬溥吚碚摚ㄓ⑽陌妫吩谥v述了quillen復配邊方法后,接著在固定域的光滑變量范疇上引進有向上同調理論的觀點,證明了這樣一個理論范的存在性叫做代數配邊。書中也包括了一些計算和應用案例。
1cobordismandorientedcohomology
1.1orientedcohomologytheories
1.2algebraiccobordism
1.3relationswithcomplexcobordism
2thedefinitionofalgebraiccobordism
2.1orientedborel-moorefunctors
2.2orientedfunctorsofgeometrictype
2.3someelementaryproperties
2.4theconstructionofalgebraiccobordism
2.5somecomputationsinalgebraiccobordism
3fundamentalpropertiesofalgebraiccobordism
3.1divisorclasses
3.2localization
3.3transversality
3.4homotopyinvariance
3.5theprojectivebundleformula
3.6theextendedhomotopyproperty
4algebraiccobordismandthelazardring
4.1weakhomologyandchernclasses
4.2algebraiccobordismandk-theory
4.3thecobordismringofapoint
4.4degreeformulas
4.5comparisonwiththechowgroups
5orientedborel-moorehomology
5.1orientedborel-moorehomologytheories
5.2otherorientedtheories