Infinite loop space structure(s) on the stable mapping class group

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

SN - 0040-9383

VL - 43

JO - Topology

JF - Topology

ER -