• Title, Summary, Keyword: equivariant cohomology

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A NOTE ON S1-EQUIVARIANT COHOMOLOGY THEORY

  • Lee, Doobeum
    • Journal of the Chungcheong Mathematical Society
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    • v.11 no.1
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    • pp.185-192
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    • 1998
  • We briefly review the $S^1$-equivariant cohomology theory of a finite dimensional compact oriented $S^1$-manifold and extend our discussion in infinite dimensional case.

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THE BOGOMOLOV-PROKHOROV INVARIANT OF SURFACES AS EQUIVARIANT COHOMOLOGY

  • Shinder, Evgeny
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1725-1741
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    • 2017
  • For a complex smooth projective surface M with an action of a finite cyclic group G we give a uniform proof of the isomorphism between the invariant $H^1(G,\;H^2(M,\;{\mathbb{Z}}))$ and the first cohomology of the divisors fixed by the action, using G-equivariant cohomology. This generalizes the main result of Bogomolov and Prokhorov [4].

EQUIVARIANT CROSSED MODULES AND COHOMOLOGY OF GROUPS WITH OPERATORS

  • CUC, PHAM THI;QUANG, NGUYEN TIEN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.4
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    • pp.1077-1095
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    • 2015
  • In this paper we study equivariant crossed modules in its link with strict graded categorical groups. The resulting Schreier theory for equivariant group extensions of the type of an equivariant crossed module generalizes both the theory of group extensions of the type of a crossed module and the one of equivariant group extensions.

EQUIARIANT K-GROUPS OF SPHERES WITH INVOLUTIONS

  • Cho, Jin-Hwan;Mikiya Masuda
    • Journal of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.645-655
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    • 2000
  • We calculate the R(G)-algebra structure on the reduced equivariant K-groups of two-dimensional spheres on which a compact Lie group G acts as a reflection. In particular, the reduced equivariant K-groups are trivial if G is abelian, which shows that the previous Y. Yang's calculation in [8] is incorrect.

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TOPOLOGICAL METHOD DOES NOT WORK FOR FRANKEL-MCDUFF CONJECTURE

  • Kim, Min Kyu
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.1
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    • pp.31-35
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    • 2007
  • In dealing with transformation group, topological approach is very natural. But, it is not sufficient to investigate geometric properties of transformation group and we need geometric method. Frankel-McDuff Conjecture is very interesting in the point that it shows struggling between topological method and geometric method. In this paper, the author suggest generalized Frankel-McDuff conjecture as a topological version of the conjecture and construct a counterexample for the generalized version, and from this we assert that topological method does not work for Frankel-McDuff Conjecture.

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