Infinite loop space structure(s) on the stable mapping class group
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Infinite loop space structure(s) on the stable mapping class group. / Wahl, Nathalie.
I: Topology, Bind 43, 2004.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Infinite loop space structure(s) on the stable mapping class group
AU - Wahl, Nathalie
N1 - Keywords: math.AT; math.GT; 55P47;32G15;55R35
PY - 2004
Y1 - 2004
N2 - Tillmann introduced two infinite loop space structures on the plus construction of the classifying space of the stable mapping class group, each with different computational advantages. The first one uses disjoint union on a suitable cobordism category, whereas the second uses an operad which extends the pair of pants multiplication (i.e. the double loop space structure introduced by E. Y. Miller). She conjectured that these two infinite loop space structures were equivalent, and managed to prove that the first delooping are the same. In this paper, we resolve the conjecture by proving that the two structures are indeed equivalent, exhibiting an explicit geometric map.
AB - Tillmann introduced two infinite loop space structures on the plus construction of the classifying space of the stable mapping class group, each with different computational advantages. The first one uses disjoint union on a suitable cobordism category, whereas the second uses an operad which extends the pair of pants multiplication (i.e. the double loop space structure introduced by E. Y. Miller). She conjectured that these two infinite loop space structures were equivalent, and managed to prove that the first delooping are the same. In this paper, we resolve the conjecture by proving that the two structures are indeed equivalent, exhibiting an explicit geometric map.
M3 - Journal article
VL - 43
JO - Topology
JF - Topology
SN - 0040-9383
ER -
ID: 9396675