論文

査読有り
2015年9月

Derived string topology and the Eilenberg-Moore spectral sequence

ISRAEL JOURNAL OF MATHEMATICS
  • Katsuhiko Kuribayashi
  • ,
  • Luc Menichi
  • ,
  • Takahito Naito

209
2
開始ページ
745
終了ページ
802
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1007/s11856-015-1236-y
出版者・発行元
HEBREW UNIV MAGNES PRESS

Let M be a simply-connected closed manifold of dimension m. Chas and Sullivan have defined (co)products on the homology of the free loop space H*(LM). F,lix and Thomas have extended the loop (co)products to those of simply-connected Gorenstein spaces over a field. We describe these loop (co)products in terms of the torsion and extension functors by developing string topology in appropriate derived categories.
In Algebraic Topology, one of the most important tools for computing the (co)homology of the space of free loops on a space is the (co)homological Eilenberg-Moore spectral sequence. Consider, over any field, the homological Eilenberg-Moore spectral sequence converging to H (*)(LM). Our description of the loop product enables one to conclude that this spectral sequence is multiplicative with respect to the Chas-Sullivan loop product and that its E (2)-term is the Hochschild cohomology of H*(M). This gives a new method to compute the loop products on H (*)(LS (m) ) and H (*)(La",P (r) ), the free loop space homology of spheres and complex projective spaces.

Web of Science ® 被引用回数 : 3

リンク情報
DOI
https://doi.org/10.1007/s11856-015-1236-y
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000364225700010&DestApp=WOS_CPL