[MBw] [w] [w] 390-8621 쌧{s3-1-1 ǗҁF \ ---ksakai(at)math.shinshu-u.ac.jp

[ u\ ] [ ܂ł̍u ] [ Z~i[Q ] [ Algebraic Toplogy: A guide to literature ] [ English ]

# u\

Title : Generalized Long-Moody functors and homology with twisted coefficients Arthur Soulié (Institut de Recherche en Mathématique Avancée, Université de Strasbourg) A-427, Faculty of Science, Shinshu University I will present the generalization of a construction due to Long and Moody gave on representations of braid groups. This associates a representation of Bn with a representation of Bn+1. This construction complexifies in a sense the initial representation: for instance, starting from a dimension one representation, one obtains the unreduced Burau representation. The generalizations of this construction to other families of groups will be done for automorphism groups of free groups, mapping class groups of orientable and non-orientable surfaces or mapping class groups of 3-manifolds. Each construction of Long and Moody defines an endofunctor, called a Long-Moody functor, on a suitable category of functors. After defining notions of polynomial functors in this context, the Long-Moody functors increase by one the degree of polynomiality. Thus, the Long-Moody constructions will provide new examples of twisted coefficients corresponding to the framework developed by Randal-Williams and Wahl in 2015 to prove homological stability with certain twisted coefficients for different families of groups, in particular the aforementioned ones.

# 2017Nx̍u

ځF The space of short ropes and the classifying space of the space of long knots \iMBwwj wA4K U (A-427)
ځF A Convenient Fibered Category for Representation Theory R ri{w5wnQwnj wA4K U (A-427)
ځF \֐̃CfAɑ΂_藝ɂ ߓ i_ސ쌧{wZj wA4K U (A-427)
ځF Symmetry of mapping classes, quadratic differentials and outer automorphisms GrikwޗȊwwAgO[vj wA4K U (A-427)
ځF Indices of Z2-spaces and Hedetniemi's conjecture Oisww@wȐwEwpUʌiPDjj wA4K U (A-427)
ځF The Picard group of a stable homotopy category ȁiVlHƍwZȁj wA4K U (A-427)
ځF Mod p homology of the classifying space of a gauge group ݖ{ Siswwj wA4K U (A-427)
ځF Configuration space of intervals with partially summable labels R ^i썂wZHwȁj wA4K U (A-427)
ځF Kontsevich's characteristic classes for Diff(S4) n ViwHwj wA4K U (A-427)
ځF Space of knots in manifolds and right A-infinity modules of configuration spaces XJ xi{wwnȁj wA4K U (A-427)

# Z~i[Q

 v MBw _ MBw _ MBw w C MBw Sw@\ MBw w MBw w HƍwZ y MBw Sw@\ y w Hw MBw w y MBw w y MBw w y MBw w y Hw@w wKxZ^[ ut Hw@w wKxZ^[ ut MBw o@w ww@ȊwȁEwpUʌ(PD) mw ㋳w ut MBww@Hwn MBww@Hwn
 [MBw] [w] [w] 390-8621 쌧{s3-1-1 ǗҁF \ ---ksakai(at)math.shinshu-u.ac.jp

[ u\ ] [ ܂ł̍u ] [ Z~i[Q ] [ Algebraic Toplogy: A guide to literature ] [ English ]

# u\

Title : Generalized Long-Moody functors and homology with twisted coefficients Arthur Soulié (Institut de Recherche en Mathématique Avancée, Université de Strasbourg) A-427, Faculty of Science, Shinshu University I will present the generalization of a construction due to Long and Moody gave on representations of braid groups. This associates a representation of Bn with a representation of Bn+1. This construction complexifies in a sense the initial representation: for instance, starting from a dimension one representation, one obtains the unreduced Burau representation. The generalizations of this construction to other families of groups will be done for automorphism groups of free groups, mapping class groups of orientable and non-orientable surfaces or mapping class groups of 3-manifolds. Each construction of Long and Moody defines an endofunctor, called a Long-Moody functor, on a suitable category of functors. After defining notions of polynomial functors in this context, the Long-Moody functors increase by one the degree of polynomiality. Thus, the Long-Moody constructions will provide new examples of twisted coefficients corresponding to the framework developed by Randal-Williams and Wahl in 2015 to prove homological stability with certain twisted coefficients for different families of groups, in particular the aforementioned ones.

# 2017Nx̍u

ځF The space of short ropes and the classifying space of the space of long knots \iMBwwj wA4K U (A-427)
ځF A Convenient Fibered Category for Representation Theory R ri{w5wnQwnj wA4K U (A-427)
ځF \֐̃CfAɑ΂_藝ɂ ߓ i_ސ쌧{wZj wA4K U (A-427)
ځF Symmetry of mapping classes, quadratic differentials and outer automorphisms GrikwޗȊwwAgO[vj wA4K U (A-427)
ځF Indices of Z2-spaces and Hedetniemi's conjecture Oisww@wȐwEwpUʌiPDjj wA4K U (A-427)
ځF The Picard group of a stable homotopy category ȁiVlHƍwZȁj wA4K U (A-427)
ځF Mod p homology of the classifying space of a gauge group ݖ{ Siswwj wA4K U (A-427)
ځF Configuration space of intervals with partially summable labels R ^i썂wZHwȁj wA4K U (A-427)
ځF Kontsevich's characteristic classes for Diff(S4) n ViwHwj wA4K U (A-427)
ځF Space of knots in manifolds and right A-infinity modules of configuration spaces XJ xi{wwnȁj wA4K U (A-427)
-->

# Z~i[Q

 v MBw _ MBw _ MBw w C MBw Sw@\ MBw w MBw w HƍwZ y MBw Sw@\ y w Hw MBw w y MBw w y MBw w y MBw w y Hw@w wKxZ^[ ut Hw@w wKxZ^[ ut MBw o@w ww@ȊwȁEwpUʌ(PD) mw ㋳w ut MBww@Hwn MBww@Hwn