The Free Loop Space Homology of (n−1)(n-1)-connected 2n2n-manifolds

Our goal in this paper is to compute the integral free loop space homology of $(n-1)$-connected $2n$-manifolds $M$, $n\geq 2$. We do this when $n\neq 2,4,8$, or when $n\neq 2$ and $\tilde H^*(M)$ has trivial cup product squares, though the techniques used here should extend to a much wider range of manifolds. We also give partial information concerning the action of the Batalin-Vilkovisky operator.Comment: JHR

The Loop Space Homotopy Type of Simply-connected Four-manifolds and their Generalizations

We determine loop space decompositions of simply-connected four-manifolds, $(n-1)$-connected $2n$-dimensional manifolds provided $n\notin\{4,8\}$, and connected sums of products of two spheres. These are obtained as special cases of a more general loop space decomposition of certain torsion-free $CW$-complexes with well-behaved skeleta and some Poincar\'{e} duality features.Comment: Adv. Math., to be publishe

Configuration Spaces and Polyhedral Products

This paper aims to find the most general combinatorial conditions under which a moment-angle complex $(D^2,S^1)^K$ is a co-$H$-space, thus splitting unstably in terms of its full subcomplexes. In this way we study to which extent the conjecture holds that a moment-angle complex over a Golod simplicial complex is a co-$H$-space. Our main tool is a certain generalisation of the theory of labelled configuration spaces.Comment: Published in Advances in Mathematics, 201

LSLS-Category of Moment-Angle Manifolds, Massey Products, and a Generalization of the Golod Property

We give various bounds for the Lusternik-Schnirelmann category of moment-angle complexes and show how this relates to vanishing of Massey products in $\mathrm{Tor}^+_{R[v_1,\ldots,v_n]}(R[K],R)$. In particular, we characterise the Lusternik-Schnirelmann category of moment-angle manifolds $\mathcal{Z}_K$ over triangulated $d$-spheres $K$ for $d\leq 2$, as well as higher dimension spheres built up via connected sum, join, and vertex doubling operations. This characterisation is given in terms of the combinatorics of $K$, the cup product length of $H^*(\mathcal{Z}_K)$, as well as a certain generalisation of the Golod property. Some applications include information about the category and vanishing of Massey products for moment-angle complexes over fullerenes and $k$-neighbourly complexes.Comment: New examples adde

Homotopy Decompositions of Looped Stiefel manifolds, and their Exponents

Let $p$ be an odd prime, and fix integers $m$ and $n$ such that $0<m<n\leq (p-1)(p-2)$. We give a $p$-local homotopy decomposition for the loop space of the complex Stiefel manifold $W_{n,m}$. Similar decompositions are given for the loop space of the real and symplectic Stiefel manifolds. As an application of these decompositions, we compute upper bounds for the $p$-exponent of $W_{n,m}$. Upper bounds for $p$-exponents in the stable range $2m<n$ and $0<m\leq (p-1)(p-2)$ are computed as well

IMPLEMENTASI KARAKTER PEDULI SOSIAL SEBAGAI PENGAMALAN NILAI-NILAI PANCASILA DALAM KOMUNITAS MOTOR VESPA : Studi Deskriptif Vespa Antique Club Indonesia Cabang Bandung

Penelitian ini bertujuan untuk mengetahui bagaimana komunitas motor vespa mengimplementasikan karakter peduli sosial sebagai pengamalan nilai-nilai Pancasila. Penelitian ini menggunakan metode studi deskriptif dengan pendekatan kualitatif. Penelitian dilakukan pada komunitas Vespa Antique Club Indonesia cabang Bandung, masyarakat dan pengurus panti asuhan. Teknik pengumpulan data yang digunakan yaitu teknik wawancara, observasi, dan dokumentasi. Hasil penelitian komunitas motor vespa melakukan kegiatan pemberian santunan, bantuan bencana alam, dan bantuan kepada kaum dhuafa. Karakter peduli sosial yang dilaksanakan ada tiga unsure yaitu, kepedulian sosial pribadi dan bersama, kepedulian berdasarkan suka dan duka, dan keadaan mendesak. Kendala yang dihadapi oleh komunitas salah satunya adalah komunikasi antara anggota. Solusi yang dilakukan dengan meningkatkan komunikasi antara anggota dengan tujuan untuk menyamakan persepsi dan pola pikir setiap anggota komunitas.;--The research aims to determine how the Vespa motorcycle Community implements social caring characters as the practice of Pancasila values. The study uses a descriptive study method with a qualitative approach. Research conducted in the community of Vespa Antique Club Indonesia Branch of Bandung, community and caretaker of orphanage. The data collection techniques used are interview techniques, observations, and documentation. The results of the research of the Vespa motorcycle Community conducted activities of compensation, relief of natural disasters, and assistance to the poor. The character of social care implemented there are three of elements namely, personal and shared social care, caring based on likes and grief, and urgent circumstances. The obstacles faced by the community are the communication between members. The solution is done by improving the communication between members with the aim to equate the perception and mindset of each community member